Non-Abelian Antibrackets

TL;DR

This paper generalizes the $ riangle$-operator and antibrackets from Abelian to non-Abelian, possibly open, algebras, with potential applications in string field theory.

Contribution

It introduces a generalized formalism for the $ riangle$-operator and antibrackets applicable to non-Abelian and open algebras of any rank.

Findings

Extended the $ riangle$-operator to non-Abelian algebras

Developed a hierarchy of antibrackets for complex algebraic structures

Discussed potential applications in string field theory

Abstract

The $\Delta$-operator of the Batalin-Vilkovisky formalism is the Hamiltonian BRST charge of Abelian shift transformations in the ghost momentum representation. We generalize this $\Delta$-operator, and its associated hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly open algebra of any rank. We comment on the possible application of this formalism to closed string field theory.