Editing Braid statistics

{{Short description|Possible statistical behavior of particles in quantum statistical mechanics}}
{{Use American English|date=January 2019}}
{{refimprove|date=November 2021}}
{{Statistical mechanics|cTopic=[[Particle statistics|Particle Statistics]]}}

In [[mathematics]] and [[theoretical physics]], '''braid statistics''' is a generalization of the [[Spin–statistics theorem|spin statistics]] of [[boson]]s and [[fermion]]s based on the concept of [[braid group]]. While for fermions (bosons) the corresponding statistics is associated to a phase gain of <math>\pi</math> (<math>2 \pi</math>) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of <math>\pi</math> under such exchange <ref>{{Cite journal|last1=Leinaas|first1=J. M.|last2=Myrheim|first2=J.|date=1977-01-01|title=On the theory of identical particles|url=https://doi.org/10.1007/BF02727953|journal=Il Nuovo Cimento B |language=en|volume=37|issue=1|pages=1–23|doi=10.1007/BF02727953|bibcode=1977NCimB..37....1L |s2cid=117277704 |issn=1826-9877|url-access=subscription}}</ref><ref>{{Cite journal|last=Wilczek|first=Frank|date=1982-10-04|title=Quantum Mechanics of Fractional-Spin Particles|url=https://link.aps.org/doi/10.1103/PhysRevLett.49.957|journal=Physical Review Letters|volume=49|issue=14|pages=957–959|doi=10.1103/PhysRevLett.49.957|bibcode=1982PhRvL..49..957W |url-access=subscription}}</ref> or even a non-trivial unitary transformation in the Hilbert space (see [[Anyon#Non-abelian anyons|non-Abelian anyons]]). A similar notion exists using a [[loop braid group]].

== Plektons ==
Braid statistics are applicable to theoretical particles such as the two-dimensional [[Anyon|anyons]] and plektons.

A '''plekton''' is a hypothetical type of [[particle]] that obeys a different style of [[quantum statistics|statistics]] with respect to the interchange of [[identical particles]]. It obeys the causality rules of [[algebraic quantum field theory]], 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.<ref>{{cite journal|last1=Fredenhagen|first1=Klaus|last2=Gaberdiel|first2=Matthias|last3=Rüger|first3=Stefan|title=Scattering states of plektons (particles with braid group statistics) in 2+1 dimensional quantum field theory|journal=Communications in Mathematical Physics|date=1996|volume=175|issue=2|pages=319–335|doi=10.1007/BF02102411|arxiv = hep-th/9410115 |bibcode = 1996CMaPh.175..319F |s2cid=14359694 }}</ref>

==See also==
* [[Braid symmetry]]
* [[Parastatistics]]
* [[Anyon]]

==References==
{{reflist}}


{{DEFAULTSORT:Braid Statistics}}
[[Category:Parastatistics]]


{{Quantum-stub}}