On algebras of gauge transformations in a general setting

TL;DR

This paper investigates the algebraic structure of gauge transformations in a general Lagrangian system, focusing on how they generate a nilpotent BRST operator, which is crucial for understanding gauge symmetries.

Contribution

It provides a general framework for describing gauge transformation algebras involving derivatives of variables and parameters, extending previous formulations.

Findings

Gauge transformations form an algebra if they generate a nilpotent BRST operator.

The framework accommodates derivatives of arbitrary order in gauge parameters.

It offers a unified approach to gauge symmetries in fiber bundle systems.

Abstract

We consider a Lagrangian system on a fiber bundle and its gauge transformations depending on derivatives of dynamic variables and gauge parameters of arbitrary order. We say that gauge transformations form an algebra if they generate a nilpotent BRST operator.