Poisson structures in BRST-antiBRST invariant Lagrangian formalism

TL;DR

This paper demonstrates how operators in the triplectic formalism relate to anti-Hamiltonian vector fields derived from Poisson brackets, enabling explicit algebra construction and linking Lagrangian and Hamiltonian BRST quantization.

Contribution

It provides a novel realization of the triplectic algebra using arbitrary Poisson brackets and constructs an even supersymplectic structure on the field-antifield space.

Findings

Operators V^a are anti-Hamiltonian vector fields.

The triplectic algebra can be explicitly realized from a Poisson bracket.

A supersymplectic structure can be established on the entire field-antifield space.

Abstract

We show that the specific operators V^a appearing in the triplectic formalism can be viewed as the anti-Hamiltonian vector fields generated by a second rank irreducible Sp(2) tensor. This allows for an explicit realization of the triplectic algebra being constructed from an arbitrary Poisson bracket on the space of the fields only, equipped by the flat Poisson connection. We show that the whole space of fields and antifields can be equipped with an even supersymplectic structure when this Poisson bracket is non-degenerate. This observation opens the possibility to provide the BRST/antiBRST path integral by a well-defined integration measure, as well as to establish a direct link between the Sp(2) symmetric Lagrangian and Hamiltonian BRST quantization schemes.