Quantum antibrackets

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 Δ-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.