Discretization of Virasoro Algebra

TL;DR

This paper introduces a q-discretization of the Virasoro algebra, derived from the Moyal bracket algebra, providing a quantum deformation distinct from quantum groups, along with a free field representation.

Contribution

It presents a novel q-discretization of the Virasoro algebra and constructs its representation using q-parametrized free fields, expanding the algebraic framework.

Findings

Q-discretization reduces to the classical Virasoro algebra as q approaches 1.

A new quantum deformation of the Virasoro algebra is established from the Moyal bracket.

Representation via q-parametrized free fields is demonstrated.

Abstract

A $q$-discretization of \vi\ algebra is studied which reduces to the ordinary \vi\ algebra in the limit of $q \ra 1$. This is derived starting from the Moyal bracket algebra, hence is a kind of quantum deformation different from the quantum groups. Representation of this new algebra by using $q$-parametrized free fields is also given.