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; 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. Fermions obey the Fermi–Dirac statistics, while bosons obey the Bose–Einstein statistics. In the language of quantum mechanics this is formulated as the behavior of multiparticle states under the exchange of particles. This is in particular for a two-particle state with indistinguishable particles (in Dirac notation):

where the first entry in |…⟩ is the state of particle 1, and the second entry is the state of particle 2 (so, for example, the left-hand side is read as "particle 1 is in state ψ₁ and particle 2 in state ψ₂"). Here the "+" corresponds to the particles being bosons, and the "−" to the particles being fermions (composite states of fermions and bosons or distinct particle types are irrelevant, since that would make them distinguishable).

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