Comments on the Covariant Sp(2)-Symmetric Lagrangian BRST Formalism

TL;DR

This paper provides a geometric interpretation of the covariant Sp(2)-symmetric quantization formalism, revealing that the even Poisson bracket arises naturally from solutions to the classical master equation, connecting it to conventional BRST methods.

Contribution

It offers a simple geometric perspective on triplectic quantization, showing the emergence of the even Poisson bracket and its relation to traditional Lagrangian BRST formalism.

Findings

Any solution of the classical master equation generates an even Poisson bracket.

Features of triplectic quantization align with aspects of conventional Lagrangian BRST quantization.

The appearance of an even Poisson bracket is not unique to triplectic quantization.

Abstract

We give a simple geometrical picture of the basic structures of the covariant $Sp(2)$ symmetric quantization formalism -- triplectic quantization -- recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry.