Quon

Quon refers to a class of hypothetical quantum particles that obey quon statistics, a one-parameter generalization of quantum statistics that interpolates between Bose-Einstein and Fermi-Dirac statistics. In the quon formalism, the creation and annihilation operators satisfy the relation a_k a_l† − q a_l† a_k = δ_kl, with q a real number between -1 and 1. The cases q = 1 and q = -1 reproduce standard bosons and fermions, respectively. For -1 < q < 1, the statistics are intermediate in character, and they lead to a continuous spectrum of exchange phases and modified permutation symmetries of multi-particle states. The quon algebra affects the structure of the Hilbert space and correlation functions, and it serves as a theoretical tool for exploring how deviations from conventional statistics would influence quantum many-body systems and quantum field theories.

Physical realization of quons remains unobserved; the framework is primarily of theoretical interest. The approach faces challenges, including potential issues with locality and the positivity of norms in the associated Fock space for certain values of q, which constrain the physical viability of quon models. Quon statistics are related to, but distinct from, other generalized statistics such as anyons in two dimensions and parastatistics. In discussions of quantum statistics, quons provide a conceptual bridge between the familiar bosonic and fermionic descriptions and offer a lens for examining how statistical principles shape quantum behavior.