Some Rigorous Results on Symmetry Breakings in Gauge QFT

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-convergence of the perturbative series, trivialy results for the ${\text{ph}}^4$ model and related models etc.). We shall briefly discuss sone non-perturbative results concerning the crucial role and realization of symmetry breakings in the Standard Model.