Hery Randriamaro - A Deformed Quon Algebra

cm:9491 - Communications in Mathematics, December 31, 2019, Volume 27 (2019), Issue 2 - https://doi.org/10.2478/cm-2019-0010
A Deformed Quon Algebra

Authors: Hery Randriamaro

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 a j , l a i , k † = q a i , k † a j , l + q β k , l δ i , 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 a i,k’s and a i , 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.

Volume: Volume 27 (2019), Issue 2
Published on: December 31, 2019
Imported on: May 11, 2022
Keywords: General Mathematics,[MATH]Mathematics [math]