Unification of parastatistics defined as triple operator algebras

Abstract

We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them as a normal ordered expansion of creation and annihilation operators. We discuss several examples of parastatistics, particularly Okubo's and Palev's parastatistics connected to many-body Wigner quantum systems. We relate them to the notion of extended Haldane statistics.

18 pages, no figures, LaTex, some references added, to appear in Int.J.Mod.Phys.A

References in corpus (2)

• Permutation Invariant Statistics, Duality and Simple Interpolations
• Parastatistics as Examples of the Extended Haldane Statistics

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• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model