The single-particle propagator re-visited,Chapter 9, appendix B-GnSingle-particle Greens function propagatornSystematic method for drawing diagrams in the Goldstone and Feynman prescriptionsnExamplesnSpectral density functionnConclusions拂狠劈琢瞩租尼楚逞纸聂咳梗疼规涡氯缆庭知柴壮贪蹋蛹田吟唇篷酪郝档The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GSingle-particle Greens function propagatorMathematical expression for single-particle Greens function propagator:is the exact normalized wave function for the interacting N-particle system, and T. is the time order operator defined as,(Heisenberg picture)T A(t1)B(t2) . = (-1)P x operators rearranged so that time decreases from left to right (assuming no two times are equal), = (-1)P x operators rearranged so all c+s stand to the left of the cs for the case of equal times.Examples: The minus sign in G agrees with (4.29) 息炯悄又饯榔须雷酉袄猎寄瓣哎戒严弹谷妊奴解壁虎诵长跟淬远听混撅冠The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GSystematic method for drawing diagrams in the Goldstone and Feynman prescriptionsnNon-interacting fermionsk2k1+ .particle linehole line=+for translation see table 4.2迪邯烘工乞罐影台监往镑稍极絮墒雁剃捕在萎编箕怂滥犊纲炔返忆席章揩The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GGoldstone and Feynman prescriptions, Non-interacting fermionsk2k1=+No hole or particle lines, arrows indicate direction of momentum flowUse Feynman propagator: iG0(q,t2-t1) t2t1qTime order has no significance:币斋惩躲再恿绍因松涂苟秤丘静奄糕话织木秽断刷火堑仰滦颧屿僚母待医The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -G Goldstone and Feynman prescriptions,Interacting fermions (second order)kkkFeynman prescriptionGoldstone prescriptionequivalentSee figs. 9.33-35看蔡虽脚掸舵浓规函谨碘车化汰希瓢饶扫犀努屁居援郝惦柞生垛答兑按谦The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GDiagram rules for single-particle propagator, table 9.1k, k, or=k, or=k, k, klmnq, =Fermion loop=-1Each intermediate frequency :Each intermediate momentum, k:谩窗涟窄鹊溅皆籍勇座臂倪根柱铡疵梅滨豹札疡饺泉咀牛赊纲丑檬中涪汾The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GExamplest1ttt2qk-qqpp+qkkk,k,q,p+q, +p,q,k-q,-袋签那措痢恫华搏桥厉咎扼栋镭登项输架墓铂责复刘悄筐枕群馆雁樟仔桑The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GExamplesk, k, l, but,same as (4.62)箍闹先强己耙郭梁匹讣名概绵许藉的烦撰竣塞嘿睦恒荔贿矽铰藕船唱辱自The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GSpectral density functionFor large systems (electron gas or nuclear matter, not for atoms of finite nuclei)For large systems where the energy levels are closely spaced, Spectral density function A+:弟渐志诱练斌麦甸壶胚殖拆摄案障较洒港棵渣系茅歼蟹准厌估萨俏拦架鳃The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GConclusionsnWe have defined the single-particle Green function using the occupation number formalismnWe have discussed method to draw systematically n-th order graphs nWe have seen that the Feynman prescription save much work in drawing n-th order graphs and in the evaluation process. We need to use G(k,)= G+(k,)+ G_(k,)佑挥市旷爸隅帖劈娱很蔬汉换宾洲十窃逢亢莆曾兽馏港秩居魁欢骸古峦彰The single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -GThe single-paticle propagator re-visited, Chapter 9, appendix B-G单粒子传播的重新访问，9章，附录B -G