A Deformed Quon Algebra

• Main Author: Randriamaro Hery
• Format: Article
• Language: English
• Published: Sciendo 2019-12-01
• Series: Communications in Mathematics
• Subjects: quon algebra; infinite statistics; hilbert space; colored permutation group; 05e15; 81r10; 15a15
• Online Access: https://doi.org/10.2478/cm-2019-0010

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 ai,k, (i, k) ∈ ℕ* × [m], on an infinite dimensional vector space satisfying the deformed q-mutator relations aj,lai,k†=qai,k†aj,l+qβk,lδi,j{a_j}_{,l}a_{i,k}^\dagger = qa_{i,k}^\dagger{a_{j,l}} + {q^{{\beta _{k,l}}}}{\delta _{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 ai,k†a_{i,k}^\dagger ‘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.