Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory

TL;DR

This paper proves the gauge invariance of causal Yang-Mills theory by introducing a gauge-factor group and demonstrating that local terms can be expressed as divergences, ensuring the theory's consistency.

Contribution

It introduces the gauge-factor group concept and systematically shows all local terms in causal Yang-Mills theory are gauge trivial or zero, establishing gauge invariance.

Findings

Gauge-factor group is defined in the style of gauge cohomology.

All local operator distributions are gauge trivial or zero.

Gauge invariance of causal Yang-Mills theory is proven.

Abstract

In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.