Consistent Interactions in terms of the Generalized Fields Method

TL;DR

This paper introduces a method using generalized fields to construct gauge-preserving interactions, simplifying the solution of descent equations in cohomological analysis across various theories.

Contribution

It presents a novel approach that streamlines finding consistent gauge interactions via the generalized fields method, aligning with cohomological results.

Findings

Successfully applied to spin-1 gauge fields in 3 and 4 dimensions

Reproduces known results in BF theory and antisymmetric tensor fields

Simplifies solving descent equations in gauge theory analysis

Abstract

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method of solving the Batalin-Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to spin-1 gauge field in 3 and 4 dimensions, to free BF theory in 2-d and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.