The effective action and quantum gauge transformations

TL;DR

This paper investigates the local symmetry transformations of the quantum effective action in gauge theories, revealing additional symmetries and constructing simplified gauge generators, including for Yang-Mills theory.

Contribution

It identifies new symmetry transformations of the quantum effective action and proposes a natural generalization for rank one theories, simplifying gauge generator construction.

Findings

Derived local symmetry transformations for quantum effective actions.

Reproduced DeWitt's result for Yang-Mills theory.

Proposed a generalization for rank one gauge theories.

Abstract

The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can be used for construction simple gauge generators. For example, for the Yang-Mills theory the classically invariant effective action is obtained, reproducing DeWitt's result. For rank one theories a natural generalization is proposed.