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 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 quantum mechanics, there can exist indistinguishable particles. Unlike in classical mechanics, where each particle is labeled by a distinct state vector ψ i {displaystyle psi _{i}} , and different configurations of the set of ψ i {displaystyle psi _{i}} s correspond to different many-body states, in quantum mechanics, the particles are identical, such that exchanging the states of two particles, i.e. ψ i ↔ ψ j {displaystyle psi _{i}leftrightarrow psi _{j}} , does not lead to a measurably different many-body quantum state. For example, a system with two indistinguishable particles, with particle 1 in state ψ1 and particle 2 in state ψ2, has state (in Dirac notation) | ψ 1 ψ 2 ⟩ {displaystyle left|psi _{1}psi _{2} ight angle } . Now suppose we exchange the states of the two particles, then the state of the system would be | ψ 2 ψ 1 ⟩ {displaystyle left|psi _{2}psi _{1} ight angle } . These two states should not have a measurable difference, so they should be the same vector, up to a phase factor: In space of three or more dimensions, elementary particles are either fermions or bosons, according to their statistical behaviour. Fermions obey Fermi–Dirac statistics, while bosons obey Bose–Einstein statistics. For bosons, the phase factor is 1 {displaystyle 1} , and for fermions, it is − 1 {displaystyle -1} . In particular, this is why fermions obey Pauli exclusion principle: If two fermions are in the same state, then we have