Extended BRS Symmetry and Gauge Independence in On-Shell Renormalization Schemes

TL;DR

This paper uses extended BRS symmetry to demonstrate gauge independence of fermion renormalization in QED and explores conditions for similar independence in QCD, highlighting challenges at higher loops.

Contribution

It introduces a method using extended BRS symmetry to prove gauge independence in on-shell QED and formulates a necessary condition for QCD, revealing difficulties at three-loop levels.

Findings

Gauge independence of Z2 in QED proven using extended BRS symmetry.

A necessary condition for gauge independence in QCD is formulated.

Gauge independence in QCD faces challenges at three-loop calculations.

Abstract

Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant $Z_2$ in on-shell QED renormalization schemes. A necessary condition for gauge independence of $Z_2$ in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD.