Off-shell renormalization of the massive QED in the unitary gauge

TL;DR

This paper investigates the off-shell renormalization of massive QED in the unitary gauge, revealing that despite initial concerns, the Green functions are multiplicatively renormalizable, which could simplify calculations in related gauge theories.

Contribution

It demonstrates that off-shell Green functions in massive QED are multiplicatively renormalizable in the unitary gauge, clarifying the structure of ultraviolet divergences.

Findings

Off-shell Green functions are multiplicatively renormalizable in the unitary gauge.

Ultraviolet divergences affect Green functions in a trivial way.

Results may extend to Higgs theories, simplifying loop calculations.

Abstract

Despite its simplicity, the unitary gauge is not a popular choice for practical loop calculations in gauge theories, due to the lack of off-shell renormalizability. We study the renormalization properties of the off-shell Green functions of the elementary electron fields in the massive QED, in order to elucidate the origin and structure of the extra ultraviolet divergences which exist only in the unitary gauge. We find that all these divergences affect the Green functions in a trivial way such that in coordinate space the off-shell Green functions are in fact multiplicatively renormalizable. This result may generalize to the abelian and non-abelian Higgs theories, for which the unitary gauge might bring much simplification to the loop calculations.