1003:
515:
524:
160:. In such cases, it is the real part of this self-energy that is identified with the physical self-energy (referred to above as particle's "self-energy"); the inverse of the imaginary part is a measure for the lifetime of the particle under investigation. For clarity, elementary excitations, or
172:
of the underlying many-particle system, which only momentarily, if at all, behave like those specific to isolated particles; the above-mentioned lifetime is the time over which a dressed particle behaves as if it were a single particle with well-defined momentum and energy.
628:
calculations. Self-energies also find extensive application in the calculation of particle transport through open quantum systems and the embedding of sub-regions into larger systems (for example the surface of a semi-infinite crystal).
153:), one retains a contribution to the self-energy operator (in, for instance, the momentum-energy representation). Using a small number of simple rules, each Feynman diagram can be readily expressed in its corresponding algebraic form.
71:, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a
507:
349:
200:
778:
387:
133:
times this value). In this, or other representations (such as the space-time representation), the self-energy is pictorially (and economically) represented by means of
255:
281:
226:
57:
444:
130:
414:
617:
771:
747:
732:
706:
168:), in interacting systems are distinct from stable particles in vacuum; their state functions consist of complicated superpositions of the
64:
663:
1006:
724:
1028:
878:
764:
801:
1038:
137:, such as the one shown below. In this particular diagram, the three arrowed straight lines represent particles, or particle
1033:
578:
169:
928:
811:
547:
949:
888:
816:
625:
452:
605:
297:
842:
156:
In general, the on-the-mass-shell value of the self-energy operator in the momentum-energy representation is
787:
964:
100:
974:
638:
33:
918:
613:
601:
179:
84:
80:
36:, the energy that a particle has as a result of changes that it causes in its environment defines
984:
959:
883:
357:
944:
913:
743:
728:
720:
702:
231:
145:) the left-most and the right-most straight lines in the diagram shown below (these so-called
717:
The Field
Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics
260:
205:
83:) and lifetime. Self-energy is especially used to describe electron-electron interactions in
42:
979:
862:
658:
419:
161:
115:
72:
392:
923:
908:
806:
648:
559:
539:
134:
112:
954:
543:
165:
157:
68:
1022:
609:
288:
150:
76:
514:
17:
570:
149:
lines correspond to prescribed values for, for instance, momentum and energy, or
893:
857:
832:
569:
Neutral particles with internal quantum numbers can mix with each other through
563:
75:
context, self-energy is used to describe interaction induced renormalization of
969:
898:
653:
643:
138:
590:
573:
production. The primary example of this phenomenon is the mixing of neutral
756:
562:; they do undergo mass renormalization through the renormalization of the
852:
837:
555:
551:
847:
597:
of an ion is the energy associated with the field of the ion itself.
531:
88:
60:
228:) is related to the bare and dressed propagators (often denoted by
67:, due to interactions between the particle and its environment. In
577:. Under appropriate simplifying assumptions this can be described
535:
141:, and the wavy line a particle-particle interaction; removing (or
546:
protects them from getting a mass. This is a consequence of the
574:
523:
760:
689:
A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinski (1963):
111:) in the momentum-energy representation (more precisely, to
87:. Another example of self-energy is found in the context of
691:
Methods of
Quantum Field Theory in Statistical Physics
679:(McGraw-Hill, New York, 1971); (Dover, New York, 2003)
99:
Mathematically, this energy is equal to the so-called
455:
422:
395:
360:
300:
263:
234:
208:
182:
118:
45:
59:, and represents the contribution to the particle's
937:
871:
825:
794:
501:
438:
408:
381:
343:
275:
249:
220:
194:
124:
51:
29:Energy quantum particles contribute to themselves
699:Quantum Field Theory in Condensed Matter Physics
608:physics self-energies and a myriad of related
772:
740:The Embedding Method for Electronic Structure
8:
701:(2nd ed.). Cambridge University Press.
91:softening due to electron-phonon coupling.
176:The self-energy operator (often denoted by
779:
765:
757:
502:{\displaystyle \Sigma =G_{0}^{-1}-G^{-1}.}
487:
471:
466:
454:
427:
421:
400:
394:
370:
365:
359:
344:{\displaystyle G=G_{0}^{}+G_{0}\Sigma G.}
326:
316:
311:
299:
270:
268:
262:
244:
239:
233:
215:
213:
207:
189:
187:
181:
117:
44:
677:Quantum Theory of Many-Particle Systems
354:Multiplying on the left by the inverse
119:
719:(Routledge Chapman & Hall 2004);
7:
618:Green's function (many-body theory)
622:interacting low-energy excitations
456:
332:
184:
46:
25:
1007:Template:Quantum mechanics topics
675:A. L. Fetter, and J. D. Walecka,
1002:
1001:
879:Anomalous magnetic dipole moment
693:Englewood Cliffs: Prentice-Hall.
522:
513:
103:value of the proper self-energy
686:(Westview Press, Boulder, 1998)
664:Wheeler–Feynman absorber theory
1:
684:Quantum Many-Particle Systems
682:J. W. Negele, and H. Orland,
612:properties are calculated by
558:get their masses through the
195:{\displaystyle \Sigma _{}^{}}
738:John E. Inglesfield (2015).
579:without quantum field theory
802:Euler–Heisenberg Lagrangian
1055:
697:Alexei M. Tsvelik (2007).
538:do not get a mass through
382:{\displaystyle G_{0}^{-1}}
993:
817:Path integral formulation
626:electronic band structure
202:, and less frequently by
985:Photon-photon scattering
250:{\displaystyle G_{0}^{}}
1029:Quantum electrodynamics
929:Ward–Takahashi identity
812:Gupta–Bleuler formalism
788:Quantum electrodynamics
276:{\displaystyle G_{}^{}}
221:{\displaystyle M_{}^{}}
52:{\displaystyle \Sigma }
503:
440:
439:{\displaystyle G^{-1}}
410:
383:
345:
283:respectively) via the
277:
251:
222:
196:
126:
125:{\displaystyle \hbar }
53:
1039:Renormalization group
950:Breit–Wheeler process
889:Klein–Nishina formula
593:, the self-energy or
504:
441:
411:
409:{\displaystyle G_{0}}
384:
346:
278:
252:
223:
197:
127:
54:
1034:Quantum field theory
639:Quantum field theory
453:
420:
416:and on the right by
393:
358:
298:
261:
232:
206:
180:
116:
43:
34:quantum field theory
18:Mass renormalization
965:DelbrĂĽck scattering
919:Vacuum polarization
843:Faddeev–Popov ghost
479:
378:
318:
272:
246:
217:
191:
960:Compton scattering
742:. IOP Publishing.
499:
462:
436:
406:
379:
361:
341:
307:
273:
264:
247:
235:
218:
209:
192:
183:
122:
49:
1016:
1015:
975:Møller scattering
945:Bhabha scattering
914:Uehling potential
863:Virtual particles
749:978-0-7503-1042-0
733:978-0-415-31002-4
708:978-0-521-52980-8
162:dressed particles
16:(Redirected from
1046:
1005:
1004:
980:Schwinger effect
781:
774:
767:
758:
753:
712:
659:GW approximation
624:on the basis of
614:Green's function
606:condensed-matter
526:
517:
508:
506:
505:
500:
495:
494:
478:
470:
445:
443:
442:
437:
435:
434:
415:
413:
412:
407:
405:
404:
389:of the operator
388:
386:
385:
380:
377:
369:
350:
348:
347:
342:
331:
330:
317:
315:
282:
280:
279:
274:
271:
269:
256:
254:
253:
248:
245:
243:
227:
225:
224:
219:
216:
214:
201:
199:
198:
193:
190:
188:
135:Feynman diagrams
131:
129:
128:
123:
107:(or proper mass
73:condensed matter
58:
56:
55:
50:
21:
1054:
1053:
1049:
1048:
1047:
1045:
1044:
1043:
1019:
1018:
1017:
1012:
1011:
989:
933:
924:Vertex function
909:Schwinger limit
884:Furry's theorem
867:
821:
807:Feynman diagram
790:
785:
750:
737:
715:A. N. Vasil'ev
709:
696:
672:
649:Renormalization
635:
587:
560:Higgs mechanism
540:renormalization
483:
451:
450:
423:
418:
417:
396:
391:
390:
356:
355:
322:
296:
295:
259:
258:
230:
229:
204:
203:
178:
177:
114:
113:
97:
95:Characteristics
41:
40:
30:
23:
22:
15:
12:
11:
5:
1052:
1050:
1042:
1041:
1036:
1031:
1021:
1020:
1014:
1013:
1010:
1009:
995:
994:
991:
990:
988:
987:
982:
977:
972:
967:
962:
957:
955:Bremsstrahlung
952:
947:
941:
939:
935:
934:
932:
931:
926:
921:
916:
911:
906:
901:
896:
891:
886:
881:
875:
873:
869:
868:
866:
865:
860:
855:
850:
845:
840:
835:
829:
827:
823:
822:
820:
819:
814:
809:
804:
798:
796:
792:
791:
786:
784:
783:
776:
769:
761:
755:
754:
748:
735:
713:
707:
694:
687:
680:
671:
668:
667:
666:
661:
656:
651:
646:
641:
634:
631:
586:
583:
544:gauge symmetry
528:
527:
519:
518:
510:
509:
498:
493:
490:
486:
482:
477:
474:
469:
465:
461:
458:
433:
430:
426:
403:
399:
376:
373:
368:
364:
352:
351:
340:
337:
334:
329:
325:
321:
314:
310:
306:
303:
285:Dyson equation
267:
242:
238:
212:
186:
166:quasi-particle
121:
96:
93:
69:electrostatics
65:effective mass
48:
28:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1051:
1040:
1037:
1035:
1032:
1030:
1027:
1026:
1024:
1008:
1000:
997:
996:
992:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
942:
940:
936:
930:
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
900:
897:
895:
892:
890:
887:
885:
882:
880:
877:
876:
874:
870:
864:
861:
859:
856:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
830:
828:
824:
818:
815:
813:
810:
808:
805:
803:
800:
799:
797:
793:
789:
782:
777:
775:
770:
768:
763:
762:
759:
751:
745:
741:
736:
734:
730:
726:
725:0-415-31002-4
722:
718:
714:
710:
704:
700:
695:
692:
688:
685:
681:
678:
674:
673:
669:
665:
662:
660:
657:
655:
652:
650:
647:
645:
642:
640:
637:
636:
632:
630:
627:
623:
619:
615:
611:
610:quasiparticle
607:
603:
598:
596:
592:
584:
582:
580:
576:
572:
567:
565:
561:
557:
553:
549:
548:Ward identity
545:
541:
537:
533:
525:
521:
520:
516:
512:
511:
496:
491:
488:
484:
480:
475:
472:
467:
463:
459:
449:
448:
447:
431:
428:
424:
401:
397:
374:
371:
366:
362:
338:
335:
327:
323:
319:
312:
308:
304:
301:
294:
293:
292:
290:
289:Freeman Dyson
287:(named after
286:
265:
240:
236:
210:
174:
171:
167:
163:
159:
154:
152:
151:four-momentum
148:
144:
140:
136:
132:
110:
106:
102:
101:on mass shell
94:
92:
90:
86:
85:Fermi liquids
82:
78:
77:quasiparticle
74:
70:
66:
62:
39:
35:
27:
19:
998:
903:
739:
716:
698:
690:
683:
676:
621:
616:methods and
599:
594:
588:
571:virtual pair
568:
529:
353:
284:
175:
155:
146:
142:
108:
104:
98:
37:
31:
26:
904:Self-energy
894:Landau pole
858:Positronium
833:Dual photon
602:solid state
595:Born energy
564:electroweak
170:eigenstates
139:propagators
81:dispersions
38:self-energy
1023:Categories
970:Lamb shift
899:QED vacuum
670:References
654:Self-force
644:QED vacuum
585:Other uses
143:amputating
999:See also:
938:Processes
826:Particles
795:Formalism
591:chemistry
489:−
481:−
473:−
457:Σ
429:−
372:−
333:Σ
185:Σ
120:ℏ
47:Σ
872:Concepts
853:Positron
838:Electron
633:See also
566:theory.
554:and the
542:because
147:external
109:operator
105:operator
556:Z-boson
552:W-boson
550:. The
446:yields
158:complex
848:Photon
746:
731:
723:
705:
532:photon
89:phonon
79:mass (
61:energy
575:kaons
536:gluon
164:(see
63:, or
744:ISBN
729:ISBN
721:ISBN
703:ISBN
604:and
534:and
530:The
257:and
620:of
600:In
589:In
291:):
32:In
1025::
727:;
581:.
780:e
773:t
766:v
752:.
711:.
497:.
492:1
485:G
476:1
468:0
464:G
460:=
432:1
425:G
402:0
398:G
375:1
367:0
363:G
339:.
336:G
328:0
324:G
320:+
313:0
309:G
305:=
302:G
266:G
241:0
237:G
211:M
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
