059<p type="texpara" tag="Body Text" et="f_0" bin="clone" >Massive Gauge Field Theory Without Higgs Mechanism Massive Gauge Field Theory Without Higgs Mechanism III. Proof of Renormalizability

TL;DR

This paper proves that a quantum massive non-Abelian gauge field theory without the Higgs mechanism is renormalizable by using Ward-Takahashi identities derived from BRST symmetry, showing it can be consistently quantized.

Contribution

It provides a rigorous proof of the renormalizability of a massive gauge field theory without Higgs, extending the understanding of gauge theories.

Findings

Renormalizability established via Ward-Takahashi identities.

Divergences can be eliminated with finite counterterms.

Renormalization constants follow the same identities as in massless theories.

Abstract

~It is shown that the quantum massive non-Abelian field theory established in the former papers is renormalizable. This conclusion is achieved with the aid of the Ward-Takahashi identities satisfied by the generating functionals which were derived in the preceding paper based on the BRST-symmetry of the theory. By the use of the Ward-Takahashi identity, it is proved that the divergences occurring in the perturbative calculations for the massive gauge field theory can be eliminated by introducing a finite number of counterterms in the effective action. As a result of the proof, it is found that the renormalization constants for the massive gauge field theory comply with the same Slavnov-Taylor identity as that for the massless gauge field theory. The latter identity is re-derived from the Ward-Takahashi identities satisfied by the gluon proper vertices and their renormalization.