Two types of q-deformed Wigner algebra

Abstract

In this paper we introduce two types of q-deformed Wigner algebras. One is q-deformation of Wigner algebra with q-reflection symmetry and another is q-deformation of Wigner algebra with reflection symmetry. For two types of q-deformed Wigner algebras, we investigate the representation and the eigenvalue of the position operator. Like q-calculus, we introduce the (q,nu)-numbers, (q,nu)-derivatives and (q,nu)-Hermite polynomials for two algebras. For the deformation parameter q = 1 - epsilon with small epsilon, we discuss the thermodynamics of the particle obeying the q-deformed Wigner algebra. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim