Lie superalgebraic framework for generalization of quantum statistics

TL;DR

This paper introduces a Lie superalgebraic framework to generalize quantum statistics, extending the known para-Bose and para-Fermi models to a broader class of Lie superalgebras, potentially enriching quantum statistical theories.

Contribution

It develops a new framework for quantum statistics based on various Lie superalgebras, expanding the mathematical foundation beyond traditional models.

Findings

Framework encompasses A(m|n), B(m|n), C(n), D(m|n) superalgebras

Generalizes existing para-Bose and para-Fermi statistics

Provides a basis for further theoretical exploration

Abstract

Para-Bose and para-Fermi statistics are known to be associated with representations of the Lie (super)algebras of class B. We develop a framework for the generalization of quantum statistics based on the Lie superalgebras A(m|n), B(m|n), C(n) and D(m|n).