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Inmathematics andtheoretical physics,braid statistics is a generalization of thespin statistics ofbosons andfermions based on the concept ofbraid group. While for fermions (bosons) the corresponding statistics is associated to a phase gain of () under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of under such exchange[1][2] or even a non-trivial unitary transformation in the Hilbert space (seenon-Abelian anyons). A similar notion exists using aloop braid group.
Braid statistics are applicable to theoretical particles such as the two-dimensionalanyons and plektons.
Aplekton is a hypothetical type ofparticle that obeys a different style ofstatistics with respect to the interchange ofidentical particles. It obeys the causality rules ofalgebraic 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.[3]
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