Relating Calculations and Renormalization in Axial and Lorentz Gauges and Gauge-independence

TL;DR

This paper compares calculations and renormalization procedures in axial and Lorentz gauges at one-loop level, demonstrating gauge-independence of the beta function and analyzing differences in wavefunction renormalization.

Contribution

It extends the formalism relating Green's functions in axial and Lorentz gauges, proving the identity of beta functions and clarifying the differences in wavefunction renormalization at one-loop.

Findings

Beta functions are identical in both gauges.

Identified diagrams contributing to wavefunction renormalization differences.

Established relations between Green's functions in axial and Lorentz gauges.

Abstract

We study futher the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the 1-loop approximation for the wavefunction renormalization and the identity of the beta-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the 1-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave-function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the beta functions in the two gauges.