Braid statistics

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 or even a non-trivial unitary transformation in the Hilbert space (see non-Abelian anyons). A similar notion exists using a loop braid group.