ON THE SUPER-RENORMALIZABILITY OF GAUGE MODELS IN THE CAUSAL APPROACH

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 behaviour 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 theory.