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 π {\displaystyle \pi } ( 2 π {\displaystyle 2\pi } ) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of π {\displaystyle \pi } under such exchange or even a non-trivial unitary transformation in the Hilbert space (see non-Abelian anyons).