Realizations of the $q$-Heisenberg and $q$-Virasoro Algebras

TL;DR

This paper provides field theoretic realizations of the $q$-Heisenberg and $q$-Virasoro algebras, deriving operator product expansions for their currents and energy momentum tensor using Sugawara construction.

Contribution

It introduces explicit field theoretic realizations of the $q$-deformed algebras and computes their operator product expansions.

Findings

Derived operator product expansions for $q$-Heisenberg and $q$-Virasoro currents

Established Sugawara construction for $q$-deformed algebras

Provided explicit field realizations

Abstract

We give field theoretic realizations of both the $q$-Heisenberg and the $q$-Virasoro algebra. In particular, we obtain the operator product expansions among the current and the energy momentum tensor obtained using the Sugawara construction.