A Holstein-Primakoff and Dyson Realizations for the Lie Superalgebra gl(m/n+1)

TL;DR

This paper extends the Holstein-Primakoff and Dyson realizations, originally for Lie algebras, to Lie superalgebras $gl(m/n+1)$, involving both Bose and Fermi operators, thus broadening the algebraic framework.

Contribution

It generalizes known realizations from Lie algebras to Lie superalgebras $gl(m/n+1)$, incorporating both Bose and Fermi operators.

Findings

Unified realization expressions for $gl(m/n+1)$

Involvement of both Bose and Fermi operators

Extension of algebraic methods to superalgebras

Abstract

The known Holstein-Primakoff and Dyson realizations for the Lie algebras $gl(n+1),\;n=1,2,\ldots$ in terms of Bose operators are generalized to the class of the Lie superalgebras $gl(m/n+1)$ for any $n$ and $m$. Formally the expressions are the same as for $gl(m+n+1)$, however both Bose and Fermi operators are involved.