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

Plektons

Braid statistics are applicable to theoretical particles such as the two-dimensional anyons and plektons.
A plekton is a hypothetical type of particle that obeys a different style of 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 D anyons being massless.