Exchange Statistics

A statistics of two identical particles 1 and 2, that is determined by a double exchange process 1→ 2 and 2→ 1. Every such exchanging yields an arbitrary phase factor q, where q is a complex number on the unit circle, i.e. . The corresponding particles are said to be in general anyons [1]. Obviously q = 1 for bosons and q = −1 for fermions. The name “quons” is also used for these particles [2]. The name “ anyons ” is then reserved to the case when q is the m-th root of unity [3]. The exchange braid statistics [4] for a system of N identical hard core particles is defined by the relation

where B:E ⊗ E→ E ⊗ E satisfy the quantum Yang–Baxter equation

and B ² = id _E .