BFV--BRST Analysis of the Classical and Quantum q-deformations of the sl(2) Algebra

TL;DR

This paper explores various constructions of the BFV--BRST charge for q-deformed sl(2) algebras, examining classical and quantum phase space deformations, and introduces a two-parameter deformation to analyze cohomology.

Contribution

It presents new methods for constructing BFV--BRST charges in q-deformed algebras and proposes a two-parameter deformation to study cohomology in combined quantum and group deformations.

Findings

Different BFV--BRST constructions for q-deformed algebras are discussed.

Deformation of phase space without generator deformation is considered.

A two-parameter deformation of sl(2) is proposed for cohomology analysis.

Abstract

BFV--BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the $q$-deformed algebra sl_q(2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. $\hbar$-q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV--BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given.