Massive Gauge Field Theory Without Higgs Mechanism II. Ward-Takahashi Identities and Proof of Unitarity

TL;DR

This paper establishes the gauge invariance, Ward-Takahashi identities, and unitarity of a massive non-Abelian gauge field theory without the Higgs mechanism, using BRST symmetry and renormalization techniques.

Contribution

It provides a rigorous proof of gauge invariance, Ward-Takahashi identities, and unitarity for a Higgsless massive gauge theory based on BRST symmetry.

Findings

Proved BRST invariance of the massive gauge theory.

Derived Ward-Takahashi identities for Green's functions.

Confirmed gauge independence and unitarity of the S-matrix.

Abstract

In our previously published papers, it was argued that a massive non-Abelian gauge field theory in which all gauge fields have the same mass can well be set up on the gauge-invariance principle. The quantization of the fields was performed by different methods. In this paper, It is proved that the quantum theory is invariant with respect to a kind of BRST-transformations. From the BRST-invariance of the theory, the Ward-Takahashi identities satisfied by the generating functionals of full Green's functions, connected Green's functions and proper vertex functions are successively derived. As an application of the above Ward-Takahashi identity, the Ward-Takahashi identity obeyed by the massive gauge boson propagator is derived and the renormalization of the propagator is discussed. Furthermore, based on the Ward-Takahashi identity, it is exactly proved that the S-matrix elements given by the quantum theory are gauge-independent and hence unitary.