A Deformed Quon Algebra

Abstract

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators a_(i,k), (i,k)∈N^∗ × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations aj,a^(\dag)(i,k) = q^(\dag)(i,k)aj,l + q^(β−k,l)δ_(i,j). We prove the realizability of our model by showing that, for suitable values of q, the vector space generated by the particle states obtained by applying combinations of ai,k's and a^(\dag)_(i,k)'s to a vacuum state |0⟩ is a Hilbert space. The proof particularly needs the investigation of the new statistic cinv and representations of the colored permutation group.