Wigner quantization and Lie superalgebra representations

Abstract

T.D. Palev laid the foundations of the investigation of Wigner quantum systems through representation theory of Lie superalgebras. His work has been very influential, in particular on my own research. It is quite remarkable that the study of Wigner quantum systems has had some impact on the development of Lie superalgebra representations. In this review paper, I will present the method of Wigner quantization and give a short overview of systems (Hamiltonians) that have recently been treated in the context of Wigner quantization. Most attention will go to a system for which the quantization conditions naturally lead to representations of the Lie superalgebra osp(1{pipe}2n). I shall also present some recent work in collaboration with G. Regniers, where generating functions techniques have been used in order to describe the energy and angular momentum contents of 3-dimensionalWigner quantum oscillators. © Springer Japan 2013.