A General Solution of the Master Equation for a Class of First Order Systems

TL;DR

This paper presents a unified, simplified method for solving the master equation in a specific class of first-order gauge theories, with applications to various fundamental physical models.

Contribution

It introduces a general, straightforward solution approach for the master equation applicable to first-order gauge theories with bilinear kinetic terms.

Findings

Solution method applied to Yang-Mills theory

Solution extended to Stueckelberg formalism for massive abelian theories

Application to relativistic particle and antisymmetric tensor fields

Abstract

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the interaction part satisfies some properties, it is possible to give the solution of the master equation in a very simple way. To clarify the general procedure we discuss its application to Yang-Mills theory, massive (abelian) theory in the Stueckelberg formalism, relativistic particle and to the self-interacting antisymmetric tensor field.