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After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v:   0` hff$Idj` [RIȺ*=zdj` 333___` }a$Idj` [RIȺ*=zd3333>?" dd@,?nK!d @  h`Fff_d <7d7 n?" dd@   @@``PP   @ ` ` p>> f ^   (    T d "` :   # ld "  :   # ?A?Stationery"   :   ^AStationery"  :   6 "  LUSQdkYkHrh7h_    6 "P  ^*  6  "p   `*^   C (A anabnr2"   <%"  :    6\* "@  n**4   Z# ??",L  8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~  H  0޽h ? [RIȺ*=zdj  Nature  0 bZ (     # l|d " -  : v  @aA ANABNR2"P    B "   :   6 "  LUSQdkYkHrh7h_    0 "   NUSQdkYkHroRh7h_   6x  "`  ^*  6d  "   `*  6 "   `*H  0޽h ? [RIȺ*=zdjs 0 0*(  r  S |    x  c $  0  H  0޽h ? ̙33y___PPT10Y+D=' i= @B +m  0 $$(  $r $ S Po    r $ S ] P  H $ 0޽h ? [RIȺ*=zdjy___PPT10Y+D=' i= @B +m  0 P$(  r  S    r  S  ,L  H  0޽h ? [RIȺ*=zdjy___PPT10Y+D=' i= @B +2  0L0 @ Z(  r  S s   r  S t ,    ZA ??@0   ZA ?? @ 5   T{ ?? 07 4MFT:  ZA ?? @p    ZA ?? F    ` ??. 8B.D.Serot, J.D.Walecka, Adv. Nucl. Phys.,Vol.16 (1986) 1$9- 6  H  0޽h ? [RIȺ*=zdj  0L0 VN`((  (r ( S    r ( S P ,L  ` ( c $A ??  ` ( c $A ??  ` ( c $A ??  ( ZA  ?? H ( 0޽h ? [RIȺ*=zdjr  0L0  p,(  ,r , S ̍   r , S  @  ` , c $A ?? ` , c $A ?? P    , TȐ ??0 j  5where  ,  `  ?? }  Mzero-point energy from vacuum  ,  ` ?? 0  h(S. A. Chin, Ann. of Phys. 108 (1977) 403$) H , 0޽h ? [RIȺ*=zdj  0L0 0(  0r 0 S ,   r 0 S  ,L   0 ZA ??p`0X " 0  ` ?? 0 HResumming all the tadpole diagram (a, b) + exchange diagram (c, d)II @< 0  `ܰ ??0`*P 8C. J. Horowitz, B. D. Serot, Nucl. Phys. A399 (1983) 529$9) ,H 0 0޽h ? [RIȺ*=zdj6  0 ]U  4(  4r 4 S $   r 4 S  ,p  ` 4 c $A ?? < B 4 S ~D>?? `  4 c $A ??     4  `H ?? `  6Where: `  4 c $A ?? #  `  4 c $A ?? @   4 T` ??"ppj CJ. Cornwall, R. Jackiw and E. Tomboulis, Phys. Rev. D10 (1974) 2428D   , H 4 0޽h ? 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After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v:  0 5-` (  r  S    r  S  ,7L    T ??G  The effective mass of and meson will be determined by minimizing the thermodynamic potential with respect to the effective mass`  c $A@ X??s 6  X`  c $A> Y??s J  Y`  c $A? u??t%   u`  c $AA x??y !  x   ` ??t< B.these requirements will generate two equationsH  0޽h ? [RIȺ*=zdj80___PPT10.0M0 0 p0(  H  0޽h ? [RIȺ*=zdj80___PPT10.P:={xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? G>M_3OTnjݰ=(x7#"0s@槐Qyw+ӆЈf)vR҉%e}A绥?l!7t1M^h5}O>V,c v۰4y,F8؀nY6Ե2(PrZD6=0O1 ?xlY|Bz<;# qz7*~ayv{S/Nr W5>oA0vlyu35m|C1:(  | x Equation Equation.30 Microsoft lQ_ 3.0 Equation EquationEquation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Micro՜.+,0    7Ļʾ8w 'Times New Roman WingdingsTahoma κNatureMicrosoft ʽ 3.0Athe CJT Calculation Beyond MFT and its Results in Nuclear MatterOutline MotivationMFT in studying nuclear matter õƬ 5 õƬ 6 õƬ 7Introduction of CJT formalism õƬ 99The application of CJT method in studying nuclear matter õƬ 11 õƬ 12 õƬ 13 õƬ 144The mean field approximation in the CJT calculation õƬ 16 õƬ 17 õƬ 18 õƬ 19 õƬ 20 õƬ 21The numerical results õƬ 23 õƬ 24BThe beyond MFT calculation and the results in the CJT calcsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBdܗ 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %N@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA( '] VnS'Yf[irtf[b 2006t^3ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayC6Summary and outlook The CJT method has been applied to study the nuclear matter. 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KA?H1: @ ㆪaM,,He` {01d++&1X +|.ǛvNh*6J` נ?ᣚ?$2?27)?/ׇOq? #2b'ܞ9pD#g +ȄJ.(3(@f3H1?:0U8VC``GW#RpeqIj. @ ] @0?2`!q'&oft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` ldX *D  @ A ? @ ABEC   =   F G _ b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayC6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v: 0 {p (    ZAC ??@T   ZAD ??TB   `d ??`  F2together with the equations of nucleon self-energy  ZAB ??+ v  ZAE ??6      ` ??7, E1these four equations can solved self-consistentlyH  0޽h ? [RIȺ*=zdj80___PPT10.P:={xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? G>M_3OTnjݰ=(x7#"0s@槐Qyw+ӆЈf)vR҉%e}A绥?l!7t1M^h5}O>V,c v۰4y,F8؀nY6Ե2(PrZD6=0O1 ?xlY|Bz<;# qz7*~ayv{S/Nr A0dFHIAKC15;(  | x Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equa/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 tion.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` ldX *D  @ A ? @ ABEC   =   F G _ b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayC6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v: 0 xp (    ZAC ??@T   ZAD ??TB   `d ??`  F2together with the equations of nucleon self-energy  ZAB ??+ v  ZAE ??6      ` ??7 B.these four equations can be numerically solvedH  0޽h ? [RIȺ*=zdj80___PPT10.P:={xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? G>M_3OTnjݰ=(x7#"0s@槐Qyw+ӆЈf)vR҉%e}A绥?l!7t1M^h5}O>V,c v۰4y,F8؀nY6Ե2(PrZD6=0O1 ?xlY|Bz<;# qz7*~ayv{S/Nr,LA0iLC1 <(   } Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` ` +D  @ A ? @ ABEC   =   F G I o b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@Ghz|: 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBdܗ 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %j@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA( '] VnS'Yf[irtf[b 2006t^3ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCE6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v:z 0 z(     fP ??< f cThe numerical results,   fHZd ??/ CWhen " nK! `  c $AF }??]~  }H  0޽h ? [RIȺ*=zdj80___PPT10.p?{xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? G>M_3OTnjݰ=(x7#"0s@槐Qyw+ӆЈf)vR҉%e}A绥?l!7t1M^h5}O>V,c v۰4y,F8؀nY6Ե2(PrZD6=0O1 ?xlY|Bz<;# qz7*~ayv{S/NxXMLA~3OPbЅ'lxA`Jhz`ÉG5!^'I 9n@ :ov.PtΛyt/_W}\ 1+}RxbXNt]AP}BF*rȏcNYPޣrMkF,$1Fqm8c*l⎥pW_R(Ͽ(4 #~>؟AhҮ?a;VׯM[ 5޷WvQT^~XP.W*|Ki zC|U*fD?̭>aFj@U-6b/s]"DeBK4 zVD!;Z,O{g5^u̙_{H3?9̳ JXEoRqaBi]W(` q ] 2Piw\hPܯqCP<\$uظQ;$Uf7]wXd^pO@+~_Pw?=?,+l͍Bb.z:0c6{ps~`VPm^Hئ^UW'1r IA cD d^%cE19<(   };~C \Jc`  ?xcdd``vfd``baV d,FYzP1n:&N! KA?H1: @ ㆪaM,,He` {01d++&1X +|.ΛT 4Hq%0qkP cQ͟d\t/W8gdcnp8VD@a۳dBH% WFGݏ~!ŏ ss1UFĤ\Y\ˠ2C 3,\|q`!r ۸HXچ`  @xcdd``vfd``baV d,FYzP1n:&N! KA?H1: @ ㆪaM, Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` ` +D  @ A ? @ ABEC   =   F G I 4 b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCE6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v:z 0 z(     fP ??< f cThe numerical results,   fHZd ??/ CWhen " nK! `  c $AG }??]~  }H  0޽h ? [RIȺ*=zdj80___PPT10.p?{xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? 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Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCE6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v: 0 80 (     fP ??< f cThe numerical results,   fHZd ??/ CWhen " nK! `  c $AF }??]~  }F  C AGs1P7 7 H  0޽h ? [RIȺ*=zdj80___PPT10.p?{xW=hA~3oL E@cI*-D$O\rư`qEHae/`a (D,b*kR" ϬQDv7o7v;'0JA{;v0"%V^>8>'!hM"Y粰L_g}s>";Jπb)+Lx"7%i# >K(=T ~887JHDxXkA~3fR1CAIRш`)4IۤJ+W*P*.Z  Wt@Y(]&й7!%ikn}yȧ\9d]6u=Ne$? 8qR^OP.Թ\ w> 9s wa{:iٿc{F3Oc? G>M_3OTnjݰ=(x7#"0s@槐Qyw+ӆЈf)vR҉%e}A绥?l!7t1M^h5}O>V,c v۰4y,F8؀nY6Ե2(PrZD6=0O1 ?xlY|Bz<;# qz7*~ayv{S/NxMOA,RA4OHx`M

N:[{xѫ=82SW|}e/A\^8R]&V_e .1&2$m|JxGjO|&\?GV {(G;N~:m_j݌+5Cq{$Q(-|/M>zɧ%&|*޺gJN|/$< "ʇ%L ވJtڂ IB"Zamqݪ?kUpw,H O\6B9LM[ftbNlj x:&r; TJMz(㼦= DBYP5A7:L';i@'2Km0 r $A dgD j`d$mE1<(    Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equa,HsBIT&CsRGBPLTEٟ IDATx=OGp+\ԶR#PB)m:'Q N0ty4QHɑLgIX(\X0 +XxA2s3Ovf_nYf9s n<3zƜ}} T}]7*N[ٖlɟ |)09{OO,?DCwܦ7Q]BJ1 9z?XT=rvdI) {s G;x?מx?tg#JE}rd#k_XR#Kw,84dw {_&:̼34/O}Ќ_?(B؎Ͽ<<p:6^=& 3:O31OG3qgL,doy3d?'`-<$- `0Z?J;o?,ݾ [?aguݞ Y2cqʷ8{?ṧo'wyˮ_gJyV/6˼_/ ]zI 8fMz^n e8W̟Z8%/5Ο؇G ìK?/_O_W?d.OxӇf]&o?e=^h׾ǏyվF_ju8_^q ?3Oit\jIW?1Ϣ~so[sȯ}q!?Cy3z@4#P6C?~^V\dQ۟D %~3E@đ^:0弃:)֧ўpg)/ˠSi_q_=H˚nﶍ~]3827jC,wo 82_ts &)I/Jԏ}$>m|%l%+5ᷯ7zFUuR~H=YYgoUGluP׏x>:/#s<4{^uP_ѧ'g#9+CO0OGc/T[%܀7;Ts=UyY?L?w@1~YxQ/+=ˇ cZaouKtg^<޿{xcdd``vfd``baV d,FYzP1n:&N! 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Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCE6Summary and outlook The CJT method has been applied to study the nuclear matter. 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Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEG6Summary and outlook The CJT method has been applied to study the nuclear matter. 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IթgON~OVߗ~|u)^i6櫞Y?~N xi3Mڤnh'ܿ O_MIPOW86~hN yb ^oOR3YA[mHѰͰ/R̿P_,ѡWo{4>~/вLˬ}SPs{|d,bs۷5o?4\O\7slgoɟQ?g;auŊt '!D/=?R?!ɿ$Ïzq#ߺq/>;.>${j uIENDB``!q\^M) "99ϰNW`  Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` p-!D  @ A ? @ ABEC   =   F G I JL< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$c\uBlAHw{yQb$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0R ʚ;i8ʚ;g4BdBd 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA* '] VnS'Yf[irtf[b 2006t^11ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook The CJT method has been applied to study the nuclear matter. 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KA?H1: @ ㆪaM,,He` @201d++&1X Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` p-!D  @ A ? @ ABEC   =   F G I JLh b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC$b$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E`2$\^M) "99ϰNWyg 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBd 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA* '] VnS'Yf[irtf[b 2006t^11ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook The CJT method has been applied to study the nuclear matter. After certain approximation the results are found to be very consistent with MFT The thermodynamical consistency has been analyzed in the CJT calculation The beyond MFT calculation will be studied in our further work.v: 0 7/(     fp@ ??<{" CWhen " nK! `  c $AN ??jw:  F  C AHs3mX H  0޽h ? [RIȺ*=zdj80___PPT10.M* 0 (  F  C AKs7 @ <F  C ALs5F  C AMs6$ q@ H  0޽h ? [RIȺ*=zdj80___PPT10.xp^RЀ3ÿ lHb@00p@$ GA @X ʐ*ѓ^ sP3i7d|< d;0Ҕ?CC*Iv".`D1zxXve(d(eH<ypʈrB(fdpڛP $,b!&FX$~Ȅ@ Q0=^&0KX)F3q<`:3@/ofrQ~q~Zէ*(\pȆgR%X4$3?ȇqXn*D+s@>&N! KAA\v0gp'f3322sq12afjKPb0``jb ,Sǰc@`𹼈;. PXg1J`|8 roL,L I9 \N<a>#d ;ȈpF՞=`Ad++FXA&0pA/Ap5kAjtȈä U*$e.p;O Ĥ\Y\pd.Wdb'τɌsѰa(ΰg/cˀ5΁f&)u1=𻁞V_@8Q$ 1@u j Om0G6Gqr;F0~y|;H1> +|._ΙvNHq%0pTW |,3Ma`xuGa32H g#jb#ܞU B*̠V5 5: ~d]R27W c\XG 4ءmLLJ% @2u(2tA4at2en /6F*bPNG  IHDR >\5‘sRGB pHYs.> WIDATx^]MhTWN,"H B.:*4. Ђva`cWZ&-Rbk5iU JR$%d\(IDžd 5B7={ݹGswιsϽ?<X 7z0"`Az{$Z:V=_|^޾isSj{*z: F=b2 f+϶nmU(    Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` p-!D  @ A ? @ ABEC   =   F G I JL< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBd 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %<@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA* '] VnS'Yf[irtf[b 2006t^11ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:  0 7/(     fp@ ??<{" CWhen " nK! `  c $AJ ??jw:  F  C AHs3mX H  0޽h ? [RIȺ*=zdj___PPT10i.M*+D=' u= @B +m  0 x$(  xr x S Հd    r x S ׀ /  H x 0޽h ? [RIȺ*=zdjy___PPT10Y+D=' u= @B +xXOA3WT1$Ep`Tœ)R>ؓ 1<`BQjAPzT/Aft%֦T}>>k;vr}}`N5d9uzkɦdO"crr3t2},,.޺Ьf]b?q 42~cq+ f9$2L sZƸSiIoX6&7HڳL&2&o>Fh'I}H:ȐJz`9>Ϙ9Vq<p9?{(V^IJ?9j&T^cot¯eHFuIۅP"R)~VYyP,Di&2VY!ɅewmǭFXz%͠;r|}5csc.CN Nr1:Cz#&)o=݋85٨b"jڱv&UV쐨GyV}HاRe|=#]þ~a.[)j] SJMS0zjjW:@z~=r (T>jU*KHLIx'Л \p z7Kq7_bC[)?. `GqFoؠ_ʠef+_OkPZ zzQw/\g\Wϟb2ɟz0=Gi.cE~2c%S?f8sV8[X2+]Q^^'95G|yM7Q}R" /&gdEr6F Hԁ9H1>(    Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` p-!D  @ A ? @ ABEC   =   F G I JL< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBd 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %<@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA* '] VnS'Yf[irtf[b 2006t^11ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:xXOA3WT1$Ep`Tœ)R>ؓ 1<`BQjAPzT/Aft%֦T}>>k;vr}}`N5d9uzkɦdO"crr3t2},,.޺Ьf]b?q 42~cq+ f9$2L sZƸSiIoX6&7HڳL&2&o>Fh'I}H:ȐJz`9>Ϙ9Vq<p9?{(V^IJ?9j&T^cot¯eHFuIۅP"R)~VYyP,Di&2VY!ɅewmǭFXz%͠;r|}5csc.CN Nr1:Cz#&)o=݋85٨b"jڱv&UV쐨GyV}HاRe|=#]þ~a.[)j] SJMS0zjjW:@z~=r (T>jU*KHLIx'Л \p z7Kq7_bC[)?. `GqFoؠ_ʠef+_OkPZ zzQw/\g\Wϟb2ɟz0=Gi.cE~2c%S?f8sV8[X2+]Q^^'95G|yM7Q}R" /&gdErF4 ]% H1>(    Equation Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 MEquation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTTvܖ 0ܖhD[SOes New RomanTTvܖ 0ܖh DWingdingsRomanTTvܖ 0ܖh0DTahomagsRomanTTvܖ 0ܖh"@DfNomagsRomanTTvܖ 0ܖh1PDNSeeOagsRomanTTvܖ 0ܖh@ .  @n?" dd@  @@`` p-!D  @ A ? @ ABEC   =   F GI JL< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?@8R ʚ;i8ʚ;g4BdBd 0bppp@ <4!d!d k 0Tu<4dddd k 0Tu <4BdBd l 0T80___PPT10 pp? %<@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA* '] VnS'Yf[irtf[b 2006t^11ga. Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.: 0 p <(    ZAC ??@T   ZAD ??TB   ` [ ??`  F2together with the equations of nucleon self-energy  ZAB ??+ v  ZAE ??6      `Ѐ ??7 B.these four equations can be numerically solved   ` ??  3(1)   `4L ??9Ca 3(2)   `Z ?? 9C  3(3)   `tf ??f 9C: 3(4)H  0޽h ? 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Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:   0` hff$Idj` [RIȺ*=zdj` 333___` }a$Idj` [RIȺ*=zd3333>?" dd@,?nK!d @  h`Fff_d <7d7 n?" dd@   @@``PP   @ ` ` p>> f ^   (    Td "` :   # ld "  :   # ?A?Stationery"   :   ^xAStationery"  :   6| "  LUSQdkYkHrh7h_    6" "P  ^*  6T( "p   `*^   C (A anabnr2"   <D,"  :    60 "@  n**4   Z' ??",L  8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~  H  0޽h ? [RIȺ*=zdj  Nature  0 bZ (     # ld " -  : v  @aA ANABNR2"P    B! "   :   6% "  LUSQdkYkHrh7h_    0X' "   NUSQdkYkHroRh7h_   6+ "`  ^*  61 "   `*  6p5 "   `*H  0޽h ? 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We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:s 0 0*(  r  S     x  c $  0  H  0޽h ? ̙33y___PPT10Y+D=' z= @B +  0 ^V (     f ??< f IThe numerical results,   f ??/ CWhen " nK! `  c $AF }??]~  }F  C AGs1. 9 z  C AIs2P ^ ,$D  0B  ZDc??jj ,$D  0H  0޽h ? [RIȺ*=zdj80___PPT10.p?+wD' z= @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +~  0 (  z  C AKs7 @ <,$D  0F  C ALs5z  C AMs6$ q@ ,$D  0H  0޽h ? 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[RIȺ*=zdj___PPT10i.P:=+D=' T = @B +  0 (  X  C      S   0    H  0޽h ? 3380___PPT10.Гm  0 (  X  C      S   0    H  0޽h ? 3380___PPT10.Gr@ uSKa+s5|C I@i oL1c?( IJ  8 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTT,ܖ 0ܖD[SOes New RomanTT,ܖ 0ܖ DWingdingsRomanTT,ܖ 0ܖ0DTahomagsRomanTT,ܖ 0ܖ"@DfNomagsRomanTT,ܖ 0ܖ1PDNSeeOagsRomanTT,ܖ 0ܖ@ .  @n?" dd@  @@`` 1%D  @ A ? @ ABEC   =   F GI JLMNOP< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?c@c8R ʚ;i8ʚ;g4MdMd\ 0ppp@ <4!d!d k 0T,<4dddd k 0T, <4BdBd l 0T80___PPT10 pp?B+ .Hubei University, WuhanO  >@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA@ '] VnS'Yf[irtf[N5uP[b/gb NmQt^ASgNAS]NeNBhg*!ac !Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:/8KLs 0 0*(  r  S Pݍ    x  c $ލ  0  H  0޽h ? ̙33y___PPT10Y+D=' = @B +rblL1c?( IJ  W Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTT,ܖ 0ܖD[SOes New RomanTT,ܖ 0ܖ DWingdingsRomanTT,ܖ 0ܖ0DTahomagsRomanTT,ܖ 0ܖ"@DfNomagsRomanTT,ܖ 0ܖ1PDNSeeOagsRomanTT,ܖ 0ܖ@ .  @n?" dd@  @@`` 1%D  @ A ? @ ABEC   =   F GI JLMNOP< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?c@c8R ʚ;i8ʚ;g4IdId 0Rppp@ <4!d!d k 0T,<4dddd k 0T, <4BdBd l 0T80___PPT10 pp?B+ .Hubei University, WuhanO  >@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA@ '] VnS'Yf[irtf[N5uP[b/gb NmQt^ASgNAS]NeNBhg*!ac !Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:/8KL 0B+ .Hubei University, Wuhan |tp  (    ZAC ??@T   ZAD ??TB    `i ??` ,$  0 F2together with the equations of nucleon self-energy  ZAB ??+ v,$D  0  ZAE ??6   ,$@  0   `Xt ??7,$  0 B.these four equations can be numerically solved   `w ??  3(1)   `{ ??9Ca 3(2)   `x ?? 9C  3(3)   `(~ ??f 9C: 3(4)H  0޽h ? [RIȺ*=zdj  ___PPT10 .P:=+y#LD, ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D&' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +p+0+0 ++0+ 0 +rC4)JL1c?( IJ  W Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTT,ܖ 0ܖD[SOes New RomanTT,ܖ 0ܖ DWingdingsRomanTT,ܖ 0ܖ0DTahomagsRomanTT,ܖ 0ܖ"@DfNomagsRomanTT,ܖ 0ܖ1PDNSeeOagsRomanTT,ܖ 0ܖ@ .  @n?" dd@  @@`` 1%D  @ A ? @ ABEC   =   F GI JLMNOP< b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&b$g5qí)2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E` 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?c@c8R ʚ;i8ʚ;g4IdId 0Rppp@ <4!d!d k 0T,<4dddd k 0T, <4BdBd l 0T80___PPT10 pp?B+ .Hubei University, WuhanO  >@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA@ '] VnS'Yf[irtf[N5uP[b/gb NmQt^ASgNAS]NeNBhg*!ac !Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:/8KL  0L0  X"(  Xr X S 4l  l r X S  l , l  X ZA ??0  X  `l ??0 w  R"Only the nucleon gap equation left## X ZA ?? iH X 0޽h ? [RIȺ*=zdjy___PPT10Y+D=' = @B +@  0L0 OG0 \(  \r \ S !l0  l r \ S "l L l  \ ZA  ??`) \  `$l ??PW  6where  \ ZA! ??    \  `(l ?? o  4and  \ ZA" ?? `I   \  `h,l ??J  SWe will obtain a set of coupled equations about the components of the self-energy TT`  \ c $A# %?? %H \ 0޽h ? 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@ ABEC   =   F GI JLMNOPh b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&$2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E`b$/6F*b j 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?c@c8R ʚ;i8ʚ;g4IdId 0Rppp@ <4!d!d k 0T,<4dddd k 0T, <4BdBd l 0T80___PPT10 pp?B+ .Hubei University, WuhanO  >@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA@ '] VnS'Yf[irtf[N5uP[b/gb NmQt^ASgNAS]NeNBhg*!ac !Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:/8KL  0L0 @ Z(  r  S 8E   r  S F ,    ZA ??@0   ZA ?? @ 5   TH ?? 07 4MFT:  ZA ?? @p F    `* ??. 8B.D.Serot, J.D.Walecka, Adv. Nucl. Phys.,Vol.16 (1986) 1$9- 6     ZAN ??Y ` )vH  0޽h ? [RIȺ*=zdjy___PPT10Y+D=' = @B +rz=L1?( IJ  W Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0 Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0%%Equation Equation.30 Microsoft lQ_ 3.0&(Equation Equation.30 Microsoft lQ_ 3.0')Equation Equation.30 Microsoft lQ_ 3.04,Equation Equation.30 Microsoft lQ_ 3.08-Equation Equation.30 Microsoft lQ_ 3.0:.Equation Equation.30 Microsoft lQ_ 3.0;/Equation Equation.30 Microsoft lQ_ 3.0<0Equation Equation.30 Microsoft lQ_ 3.0=1Equation Equation.30 Microsoft lQ_ 3.0>2Equation Equation.30 Microsoft lQ_ 3.0?3Equation Equation.30 Microsoft lQ_ 3.0@4Equation Equation.30 Microsoft lQ_ 3.0k7Equation Equation.30 Microsoft lQ_ 3.0;lQ_ Equation.30 Microsoft lQ_ 3.0<lQ_ Equation.30 Microsoft lQ_ 3.0=lQ_ Equation.30 Microsoft lQ_ 3.0X?lQ_ Equation.30 Microsoft lQ_ 3.0Y@lQ_ Equation.30 Microsoft lQ_ 3.0uAlQ_ Equation.30 Microsoft lQ_ 3.0xBlQ_ Equation.30 Microsoft lQ_ 3.0}DlQ_ Equation.30 Microsoft lQ_ 3.0FlQ_ Equation.30 Microsoft lQ_ 3.0/ 0DTimes New RomanTT,ܖ 0ܖD[SOes New RomanTT,ܖ 0ܖ DWingdingsRomanTT,ܖ 0ܖ0DTahomagsRomanTT,ܖ 0ܖ"@DfNomagsRomanTT,ܖ 0ܖ1PDNSeeOagsRomanTT,ܖ 0ܖ@ .  @n?" dd@  @@`` <41%D  @ A ? @ ABEC   =   F GI JLMNOPh b$o{.AHk(b$c/$ۿ, CS (2$v5{e+HO$b$&!~W:@x=&$2$>7a{jr ]12$"(K*̌&K i2R$NaRA G s3b$8 W6ُy85>b$0Z}[$%yڪ$6vb$!Ѯ5ՈtabPҬ2$Qb+/$ 42$2-P6y>b$- 1-}.zр~s<2$-a8ٕh$qoC AV<2$L;TU],"J=2$nSTbAoq$?b$khR?/o@2$ 쵆d poJESb$F Adb$Տ팊G/-U{b$\]J{ِh*I#b$/u LA4WD_5b$ɏJu)+_0'$y2$)T02qKib$l Q5b@n6b$ĔcM@{si/~Qb$ch]x= [: b$ '\o~h{X  b$"hOZ{G:BS7\,2$ʼL@@EBs}sucb$Gìm(`KF^Cd2$4yS 2$;/&#c+z{(b$?2u|=+I/ 22$XSSQaB2$TlXS%9yK@7 A2$:A}Vu4Cƀ=m32$2 Ml<p2$3NYߨ;42$LS\~1Db$ʨ`T "$N8u2$ʞx9b,^( R<<b$v5 b$Dxb$iR">c2$L/@b$(P 4%@_HKb$mOe8;dC2$ɇ/GahDyEib$SKt4?M{ _2".]Sb$Fȼ&ӕPK?Zb${J0E`b$/6F*b j 0e0e A@A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?c@c8R ʚ;i8ʚ;g4IdId 0Rppp@      <4!d!d k 0T,<4dddd k 0T, <4BdBd l 0T80___PPT10 pp?B+ .Hubei University, WuhanO  >@the CJT Calculation Beyond MFT and its Results in Nuclear MatterAAA@ '] VnS'Yf[irtf[N5uP[b/gb NmQt^ASgNAS]NeNBhg*!ac !Outline Motivation General introduction of CJT formalism The application of CJT method in studying nuclear matter The mean field approximation in the CJT calculation and the comparison to the usual MFT results The beyond MFT calculation and the results in the CJT calculation Summary and outlook!Z!9 MotivationMean field theory (MFT) in the study of nuclear matter QHD model, RHA, HF Develop non-perturbative calculation method beyond MFT in studying nuclear matter CJT resummation scheme48R,\ C MFT in studying nuclear matter>Quantum hadrodynamics (QHD) simple Walecka model (QHD-I) #?4  ZRelativistic Hartree approximation (RHA) propagators: G (N), ( ) , D ( ))2[ G  & Resumming all the tadpole diagram 'Z'  ,Relativistic Hartree-Fock approximation (HF) Introduction of CJT formalism.Effective action of composite operators )/ 0 Effective potential (translational invariance)118The application of CJT method in studying nuclear matter%The formulation (QHD-I model) " ZZ&   Using imaginary-time formalism "ZZ!   where     From the stationary condition!!  7 The diagrammatic representation of the gap equations88  3The mean field approximation in the CJT calculation44 Solving the gap equations according to the mean field requirements at the first step Approximation 1: replace the full meson propagators by the bare ones which means we have neglected the medium effect of the mesons4UU" (The thermodynamical potential reduced to))# 1 Assume the full nucleon propagator have the form22$ =Approximation 2: Neglect the fluctuations of the vacuum ->& SApproximation 3: Neglect the momentum dependence of the effective nucleon massCT' /Analysis of the thermodynamic consistency *0* The thermodynamic functions +The numerical results When T=0, 5( 4T=0, state equation and effective mass8 When >AThe beyond MFT calculation and the results in the CJT calculationBB(OThe medium effects of mesons will be included in a thermodynamic consistent wayCEGH6Summary and outlook $The CJT method has been applied to study the nuclear matter. We have reproduced the MFT results in the CJT calculation after taking certain approximation. The beyond mean field results are obtained by self-consistently calculating the meson effective mass. The temperature and density dependences of the effective mass has been displayed. The thermodynamic consistency has been preserved in our calculation.:/8KLn 0B+ .Hubei University, Wuhan p t(    ZAC ??@T   ZAD ??TB    `i ??` ,$  0 F2together with the equations of nucleon self-energy  ZAB ??+ v,$@ 0  ZAE ??6   ,$@ 0   `Xt ??7,$  0 B.these four equations can be numerically solved   `w ??  3(1)   `{ ??9Ca 3(2)   `x ?? 9C ,$ 0 3(3)   `(~ ??f 9C:,$ 0 3(4)H  0޽h ? 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