855:
446:
283:
The possibility that pointed out by
Coleman and E.Weinberg is, even at the classical level one tunes the mass of the scalar field to be zero, quantum correction is able to modify the effective potential, turning the point that enjoys the whole symmetry of the theory from a local minimum to a maximum,
520:
The dynamics of magnetic monopole solutions is especially simple when the theory is at BPS limit—when it can be extended to include fermionic sectors to form a supersymmetric theory. In these cases, the multi-monopole solutions can be explicitly obtained, the monopoles in a system are basically free
463:
In the original paper of
Coleman-Weinberg, as well as in the thesis of Erick Weinberg, Coleman and Weinberg discussed the renormalization of the couplings in various theories, and introduced the concept of "dimensional transmutation"—the running of coupling constants renders some coupling determined
230:
as a postdoctoral researcher. In 1975, he became an assistant professor of physics at
Columbia University. He was promoted to full professor in 1987. From 2002 to 2006, Weinberg served as the chair of Columbia University's physics department. Weinberg is still actively researching BPS monopoles and
512:
The existence of magnetic monopoles has long been an interesting and profound possibility. Such solitons could potentially explain the quantization of electric charge, as pointed out by Dirac; they can arise as the classical solutions in gauge theories, as pointed out by
Polyakov and 't Hooft; and
483:
The original proposal of inflation is, the exponentially growing phase ends via the nucleation of
Coleman-de Luccia bubbles with a low vacuum energy, these bubbles collide and thermalize, leaving a homogeneous universe with high temperature. However, as the exponential growth of the near-de Sitter
267:
Spontaneous symmetry breaking occurs in a theory when the state with the lowest energy does not have as many symmetries as the theory itself, therefore one sees degenerate vacua connected by the quotient between the symmetry of the theory and the symmetry of the state, and the particle spectrum is
586:
phase factor, therefore when considering the low energy processes the total number of degrees of freedom for n monopoles is 4n, in 4-dimensional spacetime—3 for spatial position and one for the phase factor. The dynamics can be reduced to the motion inside a 4n dimensional space with a nontrivial
279:
Usually, the way to realize spontaneous symmetry breaking is to introduce a scalar field that has a tachyonic mass parameter, classically, then the classical vacuum is the solution that stays at the bottom of the potential, with the leading quantum contribution from the uncertainty principle, the
503:
This problem called "graceful exit problem", discussed independently later by
Hawking, Moss and Stewart, then solved by the proposal of new inflation by Linde, Abrecht and Steinhardt, which makes use of Coleman-Weinberg mechanism to generate the inflation potential that satisfies slow-roll
488:"If the nucleation rate is sufficiently slow compared to the expansion rate, then the probability of any certain point in the universe to lie within an infinite volume bubble cluster will vanish, in another word, bubbles don't percolate the whole universe if the nucleation rate is small"
499:
According to these statements, if the nucleation rate of bubbles is small, we will end up with bubbles that form clusters and will not collide with each other, with the heat release from vacuum decay stored in the domain-walls, quite different from what the hot Big-Bang starts from.
268:
classified by the symmetry group of the lowest energy state (vacuum). In the case that the quotient can be parametrized by the continuous parameter(s), the local fluctuations of these parameters can be regarded as bosonic excitations (if the symmetry is bosonic), usually called
495:
The second statement suggests in a fixed coordinate any chosen bubble would be the largest in its own cluster, but this is a coordinate-dependent statement, after choosing the bubble, one can always find another coordinate in which there are bigger bubbles in the same cluster.
491:"In any pre-chosen coordinate system, any typical bubble will dominate its own cluster. In other words, for any bubble, the probability for the cluster it belongs to extend beyond this bubble by a large coordinate distance is suppressed when the nucleation rate is small"
287:
Another important point about the mechanism is, the potential remains flat with the quantum correction, if we introduce an appropriate counter-term to cancel the mass renormalization, with the minimum/maximum transition induced by a log-like term,
294:
464:
by an arbitrary energy scale, therefore although classically one starts from a theory in which there are several arbitrary dimensionless constants, one ends up with a theory with an arbitrary dimensionful parameter.
614:
maximally broken into products of U(1)'s, and argued that in some certain cases the metric can be exact—valid for crowded monopole system. This calculation is known as "Lee–Weinberg–Yi metric"
272:, which has profound implications. When coupled to gauge fields, these bosons mix into the longitudinal polarizations of the gauge fields and give masses to the fields, this is how
590:
Erick
Weinberg, with Kimyeong Lee and Piljin Yi, did a calculation for the moduli space metric in the case of well-separated monopoles, with an arbitrary large compact gauge group
612:
555:
584:
1014:
Linde, A.D. (1982). "A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems".
441:{\displaystyle V(\phi )={\frac {\lambda }{4!}}\phi ^{4}+{\frac {\lambda ^{2}\phi ^{4}}{256\pi ^{2}}}\left(\ln {\frac {\phi ^{2}}{M^{2}}}-{\frac {25}{6}}\right).}
484:
universe dilutes the bubbles nucleated, it is not obvious that the bubbles will really coalesse, in fact Guth and
Weinberg proved the following statements:
1111:
284:
and generate new minima (vacuum) at configurations with less symmetry. Therefore spontaneous symmetry breaking can have a pure quantum origin.
897:
1126:
521:
because the interaction mediated by Higgs field is cancelled by the gauge interaction. in the case of a maximally broken gauge group into
1121:
211:
1116:
1049:
Albrecht, Andreas; Steinhardt, Paul J. (1982). "Cosmology for Grand
Unified Theories with Radiatively Induced Symmetry Breaking".
93:
175:
89:
455:
introduced by Linde, Albrecht and
Steinhardt, which is still playing the dominant role among the theories of early universe.
477:
244:
179:
944:
Guth, Alan H.; Weinberg, Erick J. (1983). "Could the universe have recovered from a slow first-order phase transition?".
677:
Guth, Alan H.; Weinberg, Erick J. (1983). "Could the universe have recovered from a slow first-order phase transition?".
223:
743:
Lee, Kimyeong; Weinberg, Erick J.; Yi, Piljin (1996). "Moduli space of many BPS monopoles for arbitrary gauge groups".
624:
630:
Coleman, Sidney; Weinberg, Erick (1973). "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking".
63:
476:, Erick Weinberg discussed the possibility of ending the inflation with thermalization of vacuum bubbles in a
195:
1106:
452:
227:
1131:
1058:
1023:
988:
953:
817:
762:
715:
686:
649:
183:
1086:
979:
Hawking, S. W.; Moss, I. G.; Stewart, J. M. (1982). "Bubble collisions in the very early universe".
921:
593:
243:
Weinberg has worked on various branches in theoretical high energy physics, including the theory of
152:
148:
120:
110:
833:
807:
798:
Weinberg, Erick J.; Yi, Piljin (2007). "Magnetic monopole dynamics, supersymmetry, and duality".
786:
752:
665:
639:
199:
167:
79:
901:
778:
731:
524:
207:
159:
75:
1091:
557:, the multi-monopole solution can be viewed as weakly interacting particles, each carrying a
1066:
1031:
996:
961:
825:
770:
723:
694:
657:
203:
127:
587:
metric from the interactions among the monopoles, so called "moduli space approximation".
560:
273:
269:
280:
vacuum can be viewed as a Gaussian wave packet around the lowest point of the potential.
1062:
1027:
992:
957:
821:
766:
719:
690:
653:
171:
132:
854:
1100:
1035:
965:
837:
698:
31:
790:
669:
256:
232:
829:
625:
http://www.cup.cam.ac.uk/aus/catalogue/catalogue.asp?isbn=9781139574617&ss=exc
17:
1070:
727:
513:
the inability to detect them is one of the motivations of proposing a period of
187:
1000:
774:
661:
514:
473:
248:
782:
735:
706:
Jackiw, R.; Weinberg, Erick J. (1990). "Self-dual Chern-Simons vortices".
252:
812:
757:
644:
186:. Weinberg works on various branches in high-energy theory, including
191:
163:
849:
599:
932:
865:
623:"Classical Solutions in Quantum Field Theory" (2012)
596:
563:
527:
297:
222:
After receiving his doctorate, Weinberg went to the
451:Therefore it gives a natural arena for the idea of
126:
116:
106:
85:
71:
46:
39:
606:
578:
549:
440:
158:Weinberg received his undergraduate degree from
259:via the nucleation of quantum/thermal bubbles.
8:
468:The graceful exit problem of old inflation
36:
27:American theoretical physicist (born 1947)
811:
756:
643:
598:
597:
595:
562:
541:
526:
420:
409:
399:
393:
373:
358:
348:
341:
332:
313:
296:
210:, as well as a visiting scholar of the
889:
7:
212:Korea Institute for Advanced Study
206:. He also serves as the Editor of
25:
170:in 1973 under the supervision of
853:
1112:American theoretical physicists
517:before the hot Big-Bang phase.
251:, the theory of supersymmetric
607:{\displaystyle {\mathcal {G}}}
573:
567:
538:
531:
307:
301:
174:, with whom he discovered the
1:
922:Faculty biography at Columbia
830:10.1016/j.physrep.2006.11.002
478:cosmological phase transition
245:spontaneous symmetry breaking
180:spontaneous symmetry breaking
1036:10.1016/0370-2693(82)91219-9
966:10.1016/0550-3213(83)90307-3
699:10.1016/0550-3213(83)90307-3
224:Institute for Advanced Study
151:and professor of physics at
147:(born August 29, 1947) is a
1127:Columbia University faculty
1071:10.1103/PhysRevLett.48.1220
728:10.1103/PhysRevLett.64.2234
1148:
618:Selected articles and book
263:Coleman–Weinberg potential
176:Coleman–Weinberg mechanism
90:Coleman–Weinberg potential
29:
1122:Harvard University alumni
459:Dimensional transmutation
162:in 1968. He obtained his
138:
99:
1117:Manhattan College alumni
1001:10.1103/PhysRevD.26.2681
933:Phys Rev D staff listing
775:10.1103/PhysRevD.54.1633
550:{\displaystyle U(1)^{k}}
30:Not to be confused with
1051:Physical Review Letters
708:Physical Review Letters
662:10.1103/PhysRevD.7.1888
862:This section is empty.
608:
580:
551:
508:Lee–Weinberg–Yi metric
442:
202:in gauge theories and
94:Lee–Weinberg–Yi metric
609:
581:
552:
443:
228:Princeton, New Jersey
149:theoretical physicist
594:
579:{\displaystyle U(1)}
561:
525:
295:
255:, and the theory of
184:quantum field theory
41:Erick James Weinberg
1063:1982PhRvL..48.1220A
1028:1982PhLB..108..389L
993:1982PhRvD..26.2681H
958:1983NuPhB.212..321G
822:2007PhR...438...65W
767:1996PhRvD..54.1633L
720:1990PhRvL..64.2234J
691:1983NuPhB.212..321G
654:1973PhRvD...7.1888C
453:slow-roll inflation
196:Chern–Simons theory
153:Columbia University
121:Columbia University
111:Theoretical physics
898:"Biography on APS"
604:
576:
547:
438:
200:magnetic monopoles
168:Harvard University
80:Harvard University
64:Ossining, New York
1087:Personal homepage
1016:Physics Letters B
981:Physical Review D
946:Nuclear Physics B
882:
881:
745:Physical Review D
714:(19): 2234–2237.
679:Nuclear Physics B
632:Physical Review D
428:
415:
380:
326:
208:Physical Review D
160:Manhattan College
145:Erick J. Weinberg
142:
141:
101:Scientific career
76:Manhattan College
18:Erick J. Weinberg
16:(Redirected from
1139:
1075:
1074:
1046:
1040:
1039:
1011:
1005:
1004:
976:
970:
969:
941:
935:
930:
924:
919:
913:
912:
910:
909:
900:. Archived from
894:
877:
874:
864:You can help by
857:
850:
841:
815:
794:
760:
751:(2): 1633–1643.
739:
702:
673:
647:
613:
611:
610:
605:
603:
602:
585:
583:
582:
577:
556:
554:
553:
548:
546:
545:
472:In a paper with
447:
445:
444:
439:
434:
430:
429:
421:
416:
414:
413:
404:
403:
394:
381:
379:
378:
377:
364:
363:
362:
353:
352:
342:
337:
336:
327:
325:
314:
204:cosmic inflation
128:Doctoral advisor
60:
56:
54:
37:
21:
1147:
1146:
1142:
1141:
1140:
1138:
1137:
1136:
1097:
1096:
1092:Webpage at KIAS
1083:
1078:
1048:
1047:
1043:
1013:
1012:
1008:
978:
977:
973:
943:
942:
938:
931:
927:
920:
916:
907:
905:
896:
895:
891:
887:
878:
872:
869:
848:
806:(2–4): 65–236.
800:Physics Reports
797:
742:
705:
676:
629:
620:
592:
591:
559:
558:
537:
523:
522:
510:
470:
461:
405:
395:
386:
382:
369:
365:
354:
344:
343:
328:
318:
293:
292:
274:Higgs mechanism
270:Goldstone boson
265:
241:
220:
218:Academic career
92:
78:
72:Alma mater
67:
61:
58:
57:August 29, 1947
52:
50:
42:
35:
28:
23:
22:
15:
12:
11:
5:
1145:
1143:
1135:
1134:
1129:
1124:
1119:
1114:
1109:
1099:
1098:
1095:
1094:
1089:
1082:
1081:External links
1079:
1077:
1076:
1041:
1006:
971:
936:
925:
914:
888:
886:
883:
880:
879:
860:
858:
847:
844:
843:
842:
813:hep-th/0609055
795:
758:hep-th/9602167
740:
703:
674:
645:hep-th/0507214
627:
619:
616:
601:
575:
572:
569:
566:
544:
540:
536:
533:
530:
509:
506:
493:
492:
489:
469:
466:
460:
457:
449:
448:
437:
433:
427:
424:
419:
412:
408:
402:
398:
392:
389:
385:
376:
372:
368:
361:
357:
351:
347:
340:
335:
331:
324:
321:
317:
312:
309:
306:
303:
300:
264:
261:
240:
237:
219:
216:
172:Sidney Coleman
140:
139:
136:
135:
133:Sidney Coleman
130:
124:
123:
118:
114:
113:
108:
104:
103:
97:
96:
87:
86:Known for
83:
82:
73:
69:
68:
62:
48:
44:
43:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1144:
1133:
1130:
1128:
1125:
1123:
1120:
1118:
1115:
1113:
1110:
1108:
1107:Living people
1105:
1104:
1102:
1093:
1090:
1088:
1085:
1084:
1080:
1072:
1068:
1064:
1060:
1056:
1052:
1045:
1042:
1037:
1033:
1029:
1025:
1022:(6): 389–93.
1021:
1017:
1010:
1007:
1002:
998:
994:
990:
986:
982:
975:
972:
967:
963:
959:
955:
952:(2): 321–64.
951:
947:
940:
937:
934:
929:
926:
923:
918:
915:
904:on 2016-03-26
903:
899:
893:
890:
884:
876:
867:
863:
859:
856:
852:
851:
845:
839:
835:
831:
827:
823:
819:
814:
809:
805:
801:
796:
792:
788:
784:
780:
776:
772:
768:
764:
759:
754:
750:
746:
741:
737:
733:
729:
725:
721:
717:
713:
709:
704:
700:
696:
692:
688:
685:(2): 321–64.
684:
680:
675:
671:
667:
663:
659:
655:
651:
646:
641:
637:
633:
628:
626:
622:
621:
617:
615:
588:
570:
564:
542:
534:
528:
518:
516:
507:
505:
501:
497:
490:
487:
486:
485:
481:
479:
475:
467:
465:
458:
456:
454:
435:
431:
425:
422:
417:
410:
406:
400:
396:
390:
387:
383:
374:
370:
366:
359:
355:
349:
345:
338:
333:
329:
322:
319:
315:
310:
304:
298:
291:
290:
289:
285:
281:
277:
275:
271:
262:
260:
258:
254:
250:
246:
239:Notable works
238:
236:
234:
229:
225:
217:
215:
213:
209:
205:
201:
197:
193:
189:
185:
181:
177:
173:
169:
165:
161:
156:
154:
150:
146:
137:
134:
131:
129:
125:
122:
119:
115:
112:
109:
105:
102:
98:
95:
91:
88:
84:
81:
77:
74:
70:
65:
59:(age 77)
49:
45:
38:
33:
32:Eric Weinberg
19:
1057:(17): 1220.
1054:
1050:
1044:
1019:
1015:
1009:
987:(10): 2681.
984:
980:
974:
949:
945:
939:
928:
917:
906:. Retrieved
902:the original
892:
873:January 2013
870:
866:adding to it
861:
803:
799:
748:
744:
711:
707:
682:
678:
635:
631:
589:
519:
511:
504:conditions.
502:
498:
494:
482:
471:
462:
450:
286:
282:
278:
266:
257:vacuum decay
242:
233:vacuum decay
221:
157:
144:
143:
117:Institutions
100:
1132:1947 births
638:(6): 1888.
188:black holes
1101:Categories
908:2012-07-14
885:References
53:1947-08-29
838:119508631
515:inflation
474:Alan Guth
418:−
397:ϕ
391:
371:π
356:ϕ
346:λ
330:ϕ
316:λ
305:ϕ
249:inflation
791:18211585
783:10020838
736:10041622
253:solitons
214:(KIAS).
192:vortices
1059:Bibcode
1024:Bibcode
989:Bibcode
954:Bibcode
818:Bibcode
763:Bibcode
716:Bibcode
687:Bibcode
670:6898114
650:Bibcode
276:works.
846:Awards
836:
789:
781:
734:
668:
107:Fields
834:S2CID
808:arXiv
787:S2CID
753:arXiv
666:S2CID
640:arXiv
166:from
164:Ph.D.
779:PMID
732:PMID
178:for
66:, US
47:Born
1067:doi
1032:doi
1020:108
997:doi
962:doi
950:212
868:.
826:doi
804:438
771:doi
724:doi
695:doi
683:212
658:doi
367:256
226:in
182:in
1103::
1065:.
1055:48
1053:.
1030:.
1018:.
995:.
985:26
983:.
960:.
948:.
832:.
824:.
816:.
802:.
785:.
777:.
769:.
761:.
749:54
747:.
730:.
722:.
712:64
710:.
693:.
681:.
664:.
656:.
648:.
634:.
480:.
423:25
388:ln
247:,
235:.
198:,
194:,
190:,
155:.
55:)
1073:.
1069::
1061::
1038:.
1034::
1026::
1003:.
999::
991::
968:.
964::
956::
911:.
875:)
871:(
840:.
828::
820::
810::
793:.
773::
765::
755::
738:.
726::
718::
701:.
697::
689::
672:.
660::
652::
642::
636:7
600:G
574:)
571:1
568:(
565:U
543:k
539:)
535:1
532:(
529:U
436:.
432:)
426:6
411:2
407:M
401:2
384:(
375:2
360:4
350:2
339:+
334:4
323:!
320:4
311:=
308:)
302:(
299:V
51:(
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.