Not to be confused with anion, a negatively charged ion. For the American essential statistics moore pdf, see Jean Anyon. In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons.
In general, the operation of exchanging two identical particles may cause a global phase shift but cannot affect observables. Anyons are generally classified as abelian or non-abelian.
Abelian anyons have been detected and play a major role in the fractional quantum Hall effect. Non-abelian anyons have not been definitively detected, although this is an active area of research. In space of three or more dimensions, elementary particles are either fermions or bosons, according to their statistical behaviour. In the language of quantum mechanics, this is formulated as the behavior of multiparticle states under the exchange of particles.
Einstein statistics, as was first shown by Jon Magne Leinaas and Jan Myrheim of the University of Oslo in 1977. It is important to note that there is a slight abuse of notation in this shorthand expression, as in reality this wave function can be and usually is multi-valued. Such a theory obviously only makes sense in two-dimensions, where clockwise and counterclockwise are clearly defined directions. In between we have something different.