Open group transformations

TL;DR

This paper explores the quantization of open groups with involutive generators using a ghost-extended framework, deriving quantum Maurer-Cartan equations and analyzing solutions of the quantum master equation.

Contribution

It provides a detailed analysis of the quantum master equation solutions and introduces an extended formulation based on the extended BRST charge.

Findings

Quantum Maurer-Cartan equations derived from quantum connection operators.

Solutions of the quantum master equation characterized.

Extended formulation constructed with properties determined by the extended BRST charge.

Abstract

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.