135:
27:
764:
572:, where only observable quantities need to commute at spacelike separation, where anyons follow the stronger rules of traditional quantum field theory; this leads, for example, to (2+1)D anyons being massless.
705:
Fredenhagen, Klaus; Gaberdiel, Matthias; RĂĽger, Stefan (1996). "Scattering states of plektons (particles with braid group statistics) in 2+1 dimensional quantum field theory".
503:
523:
480:
421:
215:
805:
91:
63:
414:
70:
249:
110:
44:
257:
177:
77:
829:
569:
407:
48:
505:) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of
59:
182:
447:
172:
167:
798:
187:
241:
824:
303:
225:
149:
37:
84:
791:
320:
126:
525:
under such exchange or even a non-trivial unitary transformation in the
Hilbert space (see
462:. While for fermions (Bosons) the corresponding statistics is associated to a phase gain of
724:
679:
624:
485:
363:
779:
508:
465:
8:
565:
439:
358:
348:
160:
728:
683:
628:
740:
714:
648:
561:
233:
667:
771:
652:
640:
541:
Braid statistics are applicable to theoretical particles such as the two-dimensional
383:
325:
744:
732:
687:
632:
530:
378:
353:
368:
330:
310:
526:
775:
691:
586:
581:
373:
280:
192:
144:
818:
644:
393:
16:
Possible statistical behavior of particles in quantum statistical mechanics
459:
435:
388:
290:
285:
275:
736:
719:
636:
134:
612:
26:
557:
315:
546:
455:
763:
591:
542:
451:
197:
704:
511:
488:
468:
51:. Unsourced material may be challenged and removed.
517:
497:
474:
816:
668:"Quantum Mechanics of Fractional-Spin Particles"
610:
799:
415:
806:
792:
611:Leinaas, J. M.; Myrheim, J. (1977-01-01).
422:
408:
133:
718:
111:Learn how and when to remove this message
665:
817:
707:Communications in Mathematical Physics
613:"On the theory of identical particles"
758:
331:Grand potential / Landau free energy
49:adding citations to reliable sources
20:
564:with respect to the interchange of
529:). A similar notion exists using a
13:
568:. It obeys the causality rules of
14:
841:
762:
560:that obeys a different style of
25:
36:needs additional citations for
698:
659:
604:
570:algebraic quantum field theory
1:
666:Wilczek, Frank (1982-10-04).
597:
778:. You can help Knowledge by
7:
575:
536:
446:is a generalization of the
173:Indistinguishable particles
10:
846:
757:
692:10.1103/PhysRevLett.49.957
556:is a hypothetical type of
458:based on the concept of
672:Physical Review Letters
216:Thermodynamic ensembles
168:Spin–statistics theorem
774:-related article is a
519:
499:
476:
830:Quantum physics stubs
520:
500:
498:{\displaystyle 2\pi }
477:
321:Helmholtz free energy
250:Isoenthalpic–isobaric
127:Statistical mechanics
518:{\displaystyle \pi }
509:
486:
475:{\displaystyle \pi }
466:
45:improve this article
729:1996CMaPh.175..319F
684:1982PhRvL..49..957W
629:1977NCimB..37....1L
566:identical particles
440:theoretical physics
258:Isothermal–isobaric
161:Particle statistics
737:10.1007/BF02102411
637:10.1007/BF02727953
617:Il Nuovo Cimento B
527:non-Abelian anyons
515:
495:
472:
198:Anyonic statistics
60:"Braid statistics"
787:
786:
772:quantum mechanics
432:
431:
326:Gibbs free energy
178:Maxwell–Boltzmann
121:
120:
113:
95:
837:
808:
801:
794:
766:
759:
749:
748:
722:
702:
696:
695:
663:
657:
656:
608:
531:loop braid group
524:
522:
521:
516:
504:
502:
501:
496:
481:
479:
478:
473:
444:braid statistics
424:
417:
410:
203:Braid statistics
137:
123:
122:
116:
109:
105:
102:
96:
94:
53:
29:
21:
845:
844:
840:
839:
838:
836:
835:
834:
815:
814:
813:
812:
755:
753:
752:
703:
699:
678:(14): 957–959.
664:
660:
609:
605:
600:
578:
539:
510:
507:
506:
487:
484:
483:
467:
464:
463:
448:spin statistics
428:
399:
398:
344:
336:
335:
311:Internal energy
306:
296:
295:
271:
263:
262:
242:Grand canonical
218:
208:
207:
163:
117:
106:
100:
97:
54:
52:
42:
30:
17:
12:
11:
5:
843:
833:
832:
827:
825:Parastatistics
811:
810:
803:
796:
788:
785:
784:
767:
751:
750:
720:hep-th/9410115
713:(2): 319–335.
697:
658:
602:
601:
599:
596:
595:
594:
589:
587:Parastatistics
584:
582:Braid symmetry
577:
574:
538:
535:
514:
494:
491:
471:
430:
429:
427:
426:
419:
412:
404:
401:
400:
397:
396:
391:
386:
381:
376:
371:
366:
361:
356:
351:
345:
342:
341:
338:
337:
334:
333:
328:
323:
318:
313:
307:
302:
301:
298:
297:
294:
293:
288:
283:
278:
272:
269:
268:
265:
264:
261:
260:
252:
244:
236:
228:
226:Microcanonical
219:
214:
213:
210:
209:
206:
205:
200:
195:
193:Parastatistics
190:
185:
180:
175:
170:
164:
159:
158:
155:
154:
153:
152:
150:Kinetic theory
147:
145:Thermodynamics
139:
138:
130:
129:
119:
118:
33:
31:
24:
15:
9:
6:
4:
3:
2:
842:
831:
828:
826:
823:
822:
820:
809:
804:
802:
797:
795:
790:
789:
783:
781:
777:
773:
768:
765:
761:
760:
756:
746:
742:
738:
734:
730:
726:
721:
716:
712:
708:
701:
693:
689:
685:
681:
677:
673:
669:
662:
654:
650:
646:
642:
638:
634:
630:
626:
622:
618:
614:
607:
603:
593:
590:
588:
585:
583:
580:
579:
573:
571:
567:
563:
559:
555:
550:
548:
544:
534:
532:
528:
512:
492:
489:
469:
461:
457:
453:
449:
445:
441:
437:
425:
420:
418:
413:
411:
406:
405:
403:
402:
395:
392:
390:
387:
385:
382:
380:
377:
375:
372:
370:
367:
365:
362:
360:
357:
355:
352:
350:
347:
346:
340:
339:
332:
329:
327:
324:
322:
319:
317:
314:
312:
309:
308:
305:
300:
299:
292:
289:
287:
284:
282:
279:
277:
274:
273:
267:
266:
259:
256:
253:
251:
248:
245:
243:
240:
237:
235:
232:
229:
227:
224:
221:
220:
217:
212:
211:
204:
201:
199:
196:
194:
191:
189:
186:
184:
183:Bose–Einstein
181:
179:
176:
174:
171:
169:
166:
165:
162:
157:
156:
151:
148:
146:
143:
142:
141:
140:
136:
132:
131:
128:
125:
124:
115:
112:
104:
101:November 2021
93:
90:
86:
83:
79:
76:
72:
69:
65:
62: –
61:
57:
56:Find sources:
50:
46:
40:
39:
34:This article
32:
28:
23:
22:
19:
780:expanding it
769:
754:
710:
706:
700:
675:
671:
661:
620:
616:
606:
553:
551:
540:
443:
433:
254:
246:
238:
230:
222:
202:
107:
98:
88:
81:
74:
67:
55:
43:Please help
38:verification
35:
18:
623:(1): 1–23.
460:braid group
436:mathematics
379:von Neumann
188:Fermi–Dirac
819:Categories
598:References
562:statistics
343:Scientists
304:Potentials
71:newspapers
653:117277704
645:1826-9877
513:π
493:π
470:π
374:Ehrenfest
354:Boltzmann
234:Canonical
745:14359694
576:See also
558:particle
547:plektons
537:Plektons
456:fermions
369:Einstein
316:Enthalpy
281:Einstein
725:Bibcode
680:Bibcode
625:Bibcode
554:plekton
349:Maxwell
85:scholar
743:
651:
643:
543:anyons
452:bosons
384:Tolman
270:Models
87:
80:
73:
66:
58:
770:This
741:S2CID
715:arXiv
649:S2CID
592:Anyon
394:Fermi
389:Debye
364:Gibbs
291:Potts
286:Ising
276:Debye
92:JSTOR
78:books
776:stub
641:ISSN
545:and
454:and
438:and
359:Bose
64:news
733:doi
711:175
688:doi
633:doi
450:of
434:In
255:NPT
247:NPH
239:µVT
231:NVT
223:NVE
47:by
821::
739:.
731:.
723:.
709:.
686:.
676:49
674:.
670:.
647:.
639:.
631:.
621:37
619:.
615:.
552:A
549:.
533:.
442:,
807:e
800:t
793:v
782:.
747:.
735::
727::
717::
694:.
690::
682::
655:.
635::
627::
490:2
482:(
423:e
416:t
409:v
114:)
108:(
103:)
99:(
89:·
82:·
75:·
68:·
41:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
