Quantum antibrackets

TL;DR

This paper introduces a quantum version of the classical antibracket, exploring its algebraic properties, relation to classical structures, and higher-order generalizations within the BV-quantization framework.

Contribution

It defines a quantum antibracket satisfying classical algebraic properties and introduces higher quantum antibrackets with consistent identities and rules.

Findings

Quantum antibracket mirrors classical properties

Higher quantum antibrackets satisfy Jacobi identities

Establishes relation to BV-quantization operators

Abstract

A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket as commutators to Poisson brackets. It is explained how this quantum antibracket is related to the classical antibracket and the \Delta-operator in the BV-quantization. Higher quantum antibrackets are introduced in terms of generating operators, which automatically yield all their subsequent Jacobi identities as well as the consistent Leibniz' rules.