Representation of a gauge field via intrinsic "BRST" operator

TL;DR

This paper presents a novel representation of gauge fields using an intrinsic BRST operator, providing a new perspective on Yang-Mills theory and extending to more general algebraic structures.

Contribution

It introduces a representation of matrix-valued gauge fields via an intrinsic BRST operator, generalizing the standard Yang-Mills formulation to quasigroups and involutive cases.

Findings

Reproduces the standard Yang-Mills theory using the intrinsic BRST operator.

Provides a natural counterpart to the Yang-Mills action for quasigroup/groupoid generators.

Extends the formalism to involutive matrix-valued gauge generators.

Abstract

We show that there exists a representation of a matrix valued gauge field via intrinsic "BRST" operator assigned to matrix valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang - Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.