BFV-BRST ANALYSIS OF THE CLASSICAL AND QUANTUM Q-DEFORMATIONS OF THE SL(2) ALGEBRA


DAYI O.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.27, no.1, pp.219-230, 1994 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 1994
  • Doi Number: 10.1088/0305-4470/27/1/016
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
  • Page Numbers: pp.219-230

Abstract

BFV-BRST charge for quantum algebras is not unique. Different constructions of it in classical and quantum phase space for the universal enveloping algebra of the q-deformed sl(2) are discussed. In the quantum framework a positive definite scalar product is used to introduce a co-BFV-BRST charge to study the cohomology problem by means of the techniques of the non-deformed case. 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 for sl(2). 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.