Renormalisability of the SU(n) Gauge Theory with Massive Gauge Bosons

TL;DR

This paper investigates the renormalisability of SU(n) gauge theories with massive gauge bosons, demonstrating that mass terms do not hinder the theory's renormalisability by relating it to the massless Yang-Mills case.

Contribution

It shows that adding mass to gauge bosons in SU(n) theories does not affect renormalisability, linking it to the well-understood massless Yang-Mills theory.

Findings

Mass term does not alter the ghost action compared to Landau gauge.

Mass term does not complicate the Slavnov-Taylor identity.

Renormalisability follows from that of Yang-Mills theory.

Abstract

The problem of renormalisability of the SU(n) theory with massive gauge bosons is reinverstigated in the present work. We expound that the quantization under the Lorentz condition caused by the mass term of the gauge fields leads to a ghost action which is the same as that of the usual SU(n) Yang-Mills theory in the Landau gauge. Furthermore, we clarify that the mass term of the gauge fields cause no additional complexity to the Slavnov-Taylor identity of the generating functional for the regular vertex functions and does not change the equations satisfied by the divergent part of this generating functional. Finally, we prove that the renormalisability of the theory can be deduced from the renormalisability of the Yang-Mills theory.