Wigner Quantum Oscillators

TL;DR

This paper introduces three new classes of noncanonical quantum oscillators, each associated with different Lie superalgebras, revealing unique spectral properties and connections to para-Bose statistics.

Contribution

It presents novel quantum oscillators linked to specific Lie superalgebras, expanding the understanding of noncanonical quantum systems.

Findings

sl(1/3)-oscillators have finite energy spectrum

osp(1/6)-oscillators relate to para-Bose statistics

osp(3/2)-oscillators have limited angular momentum values

Abstract

We present three groups of noncanonical quantum oscillators. The position and the momentum operators of each of the groups generate basic Lie superalgebras, namely $sl(1/3)$, $osp(1/6)$ and $osp(3/2)$. The $sl(1/3)$-oscillators have finite energy spectrum and finite-dimensions. The $osp(1/6)$-oscillators are related to the para-Bose statistictics. The internal angular momentum $s$ of the $osp(3/2)$-oscillators takes no more than three (half)integer values. In a particular representation $s=1/2$.