Some rigorous results on symmetry breakings in gauge QFT

Abstract

The extraordinary success of the Standard Model asks for a more rigorous control beyond the perturbative approach, which is affected by mathematical problems (interaction picture and canonical quantization, non-covergence of the perturbative series, triviality results for $\phi^4$ model and related models, etc.). We shall briefly discuss some non-perturbative results concerning the crucial role and realization of symmetry breakings in the Standard Model.