Wigner quantum systems (Lie superalgebraic approach)

TL;DR

This paper explores specific Wigner Quantum Systems linked to Lie superalgebras, highlighting their physical features and the noncommutative geometry underlying one of the systems.

Contribution

It introduces three new examples of Wigner Quantum Systems associated with particular Lie superalgebras and discusses their physical and geometric properties.

Findings

Examples related to $osp(1/6n)$, $sl(1/3n)$, and $sl(n/3)$ are presented.

The physical features of these systems are briefly analyzed.

Noncommutative geometry is identified in the $sl(1/3n)$ case.

Abstract

We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying geometry is noncommutative.