BRST Charge Operator for Generalized Deformed SU(2) Algebra

The BRST Charge plays a prominent role in interaction theory based on the Gauge symmetry group. In this work we find the explicit expression of the BRST charge for Generalized deformed SU(2) algebra.

BRST Charge Operator for Generalized Deformed SU(2) Algebra

The BRST Charge plays a prominent role in interaction theory based on the Gauge symmetry group. In this work we find the explicit expression of the BRST charge for Generalized deformed SU(2) algebra.

OPEN GROUP TRANSFORMATIONS WITHIN THE Sp(2)-FORMALISM

Previously we have shown that open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of the nilpotent BFV–BRST charge operator. Here we show that they may also be quantized within an Sp(2)-frame in which there are two odd anticommuting operators called Sp(2)-charges. Previous results for finite open group transformations are generalized to the Sp(2)-formalism. We show that in order to define open group transformations on the whole ghost extended space we need Sp(2)-charges in the nonminimal sector which contains dynamical Lagrange multipliers. We give an Sp(2)-version of the quantum master equation with extended Sp(2)-charges and a master charge of a more involved form, which is proposed to represent the integrability conditions of defining operators of connection operators and which therefore should encode the generalized quantum Maurer–Cartan equations for arbitrary open groups. General solutions of this master equation are given in explicit form. A further extended Sp(2)-formalism is proposed in which the group parameters are quadrupled to a supersymmetric set and from which all results may be derived.

OPEN GROUP TRANSFORMATIONS

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV–BRST charge operator. Previously we have shown that generalized quantum Maurer–Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV–BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.