On the Super-Renormalizablity of Gauge Models in the Causal Approach

TL;DR

This paper demonstrates that certain gauge models, specifically Yang-Mills and massless gravity, exhibit improved ultraviolet behavior in the causal approach, with loop contributions being coboundaries up to super-renormalizable terms, simplifying their quantum analysis.

Contribution

It proves that loop contributions in these gauge models are coboundaries, indicating better ultraviolet behavior and potential classicality, with a conjecture for higher-order extensions.

Findings

Loop contributions are coboundaries in Yang-Mills and gravity.

Yang-Mills exhibits super-renormalizable terms.

Gravity loop contributions are essentially classical.

Abstract

We consider some typical gauge models in the causal approach: Yang-Mills and pure massless gravity up to the second order of the perturbation theory. We prove that the loop contributions are coboundaries, up to super-renormalizable terms in the Yang-Mills case; this means that the ultra-violet behavior is better than expected from power counting considerations. For the pure massless gravity we prove that the loop contributions are coboundaries so the model is essentially classical. We conjecture that such a result should be true in higher orders of the perturbation theory also. This result should make easier the problem of constructive quantum field