In mathematics and theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group. While for fermions (Bosons) the corresponding statistics is associated to a phase gain of ${\displaystyle \pi }$ (${\displaystyle 2\pi }$) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of ${\displaystyle \pi }$ under such exchange ^[1][2] or even a non-trivial unitary transformation in the Hilbert space (see non-Abelian anyons). A similar notion exists using a loop braid group.

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Braid statistics are applicable to theoretical particles such as the two-dimensional anyons and their higher-dimensional analogues known as plektons.

A plekton is a hypothetical type of particle that obeys a different style of statistics with respect to the interchange of identical particles. That is, it would be neither a boson nor a fermion, but subject to a braid statistics.^[3] Such particles have been discussed as a generalization of the braid characteristics of the anyon to dimension > 2.

• Braid symmetry
• Parastatistics
• Anyon