Massive Gauge Field Theory Without Higgs Mechanism IV. Illustration of Unitarsity

TL;DR

This paper demonstrates the unitarity of a massive gauge field theory without the Higgs mechanism by calculating scattering amplitudes and showing cancellations of unphysical contributions, confirming the theory's consistency.

Contribution

It provides an explicit calculation illustrating unitarity in a Higgsless massive gauge theory using perturbation theory and the optical theorem.

Findings

Unphysical intermediate states cancel out in S-matrix elements.

Unitarity is maintained up to fourth order in perturbation.

The approach confirms the consistency of the Higgsless gauge theory.

Abstract

To illustrate the unitarity of the massive gauge field theory described in the foregoing papers, we calculate the scattering amplitudes up to the fourth order of perturbation by the optical theorem and the Landau-Cutkosky rule. In the calculations, it is shown that for a given process, if all the diagrams are taken into account, the contributions arising from the unphysical intermediate states included in the longitudinal part of the gauge boson propagator and in the ghost particle propagator are completely cancelled out with each other in the S-matrix elements. Therefore, the unitarity of the S-matrix is perfectly ensured.