Solution of the Master Equation in Terms of the Odd Time Formulation

TL;DR

This paper introduces a simplified method for solving the master equation in gauge theories using an 'odd time' formulation, streamlining the quantization process in the Batalin-Vilkovisky framework.

Contribution

It presents a novel approach to derive the minimal solution of the master equation via an odd time lagrangian and hamiltonian, simplifying the quantization procedure.

Findings

Applied to Yang-Mills theory, massive abelian theory, relativistic particle, and antisymmetric tensor field.

Demonstrated the method's effectiveness in various gauge theories.

Provided a systematic and simplified solution to the master equation.

Abstract

A systematic way of formulating the Batalin-Vilkovisky method of quantization was obtained in terms of the ``odd time'' formulation. We show that in a class of gauge theories it is possible to find an ``odd time lagrangian'' yielding, by a Legendre transformation, an ``odd time hamiltonian'' which is the minimal solution of the master equation. This constitutes a very simple method of finding the minimal solution of the master equation which is usually a tedious task. To clarify the general procedure we discussed its application to Yang-Mills theory, massive (abelian) theory in Stueckelberg formalism, relativistic particle and the self-interacting antisymmetric tensor field.