Editing Indistinguishable particles (section)

=== Fermions and bosons ===

The choice of symmetry or antisymmetry is determined by the species of particle. For example, symmetric states must always be used when describing [[photon]]s or [[helium-4]] atoms, and antisymmetric states when describing [[electron]]s or [[proton]]s.

Particles which exhibit symmetric states are called [[boson]]s. The nature of symmetric states has important consequences for the statistical properties of systems composed of many identical bosons. These statistical properties are described as [[Bose–Einstein statistics]].

Particles which exhibit antisymmetric states are called [[fermion]]s. Antisymmetry gives rise to the [[Pauli exclusion principle]], which forbids identical fermions from sharing the same quantum state. Systems of many identical fermions are described by [[Fermi–Dirac statistics]].

[[Parastatistics]] are mathematically possible, but no examples exist in nature.<ref>{{Cite journal |last1=Baker |first1=David John |last2=Halvorson |first2=Hans |last3=Swanson |first3=Noel |date=2015-12-01 |title=The Conventionality of Parastatistics |url=https://www.journals.uchicago.edu/doi/10.1093/bjps/axu018 |journal=The British Journal for the Philosophy of Science |language=en |volume=66 |issue=4 |pages=929–976 |doi=10.1093/bjps/axu018 |issn=0007-0882}}</ref>

In certain two-dimensional systems, mixed symmetry can occur. These exotic particles are known as [[anyon]]s, and they obey [[fractional statistics]]. Experimental evidence for the existence of anyons exists in the [[quantum Hall effect|fractional quantum Hall effect]], a phenomenon observed in the two-dimensional electron gases that form the inversion layer of [[MOSFET]]s. There is another type of statistic, known as [[braid statistics]], which are associated with particles known as [[plekton]]s.

The [[spin-statistics theorem]] relates the exchange symmetry of identical particles to their [[Spin (physics)|spin]]. It states that bosons have integer spin, and fermions have half-integer spin. Anyons possess fractional spin.