Once more on parastatistics

TL;DR

This paper establishes a clear equivalence between algebraic structures related to parastatistics and certain orthosymplectic Lie superalgebras, revealing more complex para-Fermi and para-Bose systems than previously known.

Contribution

It explicitly demonstrates the equivalence between parastatistics algebraic structures and orthosymplectic Lie superalgebras, and shows these superalgebras lead to more complex systems.

Findings

Explicit equivalence between parastatistics algebras and orthosymplectic superalgebras

Identification of more complex para-Fermi and para-Bose systems

Enhanced understanding of algebraic structures in quantum statistics

Abstract

Equivalence between algebraic structures generated by parastatisticstriple relations of Green (1953) and Greenberg -- Messiah (1965), and certain orthosymplectic $\mathbb{Z}_2\times \mathbb{Z}_2$-graded Lie superalgebras is found explicitly. Moreover, it is shown that such superalgebras give more complex para-Fermi and para-Bose systems then ones of Green -- Greenberg -- Messiah.