An Analogue of Holstein-Primakoff and Dyson Realizations for Lie Superalgebras. The Lie superalgebra sl(1/n)

TL;DR

This paper develops analogues of the Holstein-Primakoff and Dyson realizations specifically for the Lie superalgebra sl(1/n), extending known algebraic methods to superalgebra structures.

Contribution

It provides explicit formulations of these realizations for sl(1/n), adapting bosonic operators to fermionic ones within the superalgebra context.

Findings

Formulated Holstein-Primakoff and Dyson realizations for sl(1/n)

Revealed formal similarities with sl(n+1) algebra

Replaced Bose operators with Fermi operators in the superalgebra setting

Abstract

An analogue of the Holstein-Primakoff and of the Dyson realization for the Lie superalgebra $sl(1/n)$ is written down. The expressions are formally the same as for the Lie algebra $sl(n+1)$, however in the latter the Bose operators have to be replaced with Fermi operators.