Gauge invariant action at the ultraviolet cutoff

TL;DR

This paper demonstrates that gauge theories can be formulated with a local, BRS invariant action at the UV cutoff, using a local field transformation to relate UV and effective fields, with parameters fixed by gauge symmetry.

Contribution

It introduces a method to construct a gauge-invariant local action at the UV cutoff via a local field transformation, ensuring consistency with gauge symmetry.

Findings

Gauge-invariant UV action formulated with local fields

Field transformation parameters fixed perturbatively by gauge symmetry

Framework applicable to $SU(2)$ gauge theory

Abstract

We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry.