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^4ϕ4
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.