Open groups of constraints - Integrating arbitrary involutions

TL;DR

This paper introduces a novel quantum master equation utilizing quantum antibrackets to integrate arbitrary open groups of constraints, extending the BFV-BRST formalism to more general involutions.

Contribution

It proposes a new quantum master equation framework for open groups of constraints using quantum antibrackets, broadening the scope of the BFV-BRST approach.

Findings

Verified at the quasigroup level.

Derived integration formulas for quantum antibrackets.

Constructed a generating operator for operators in arbitrary involutions.

Abstract

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.