  Extending the scalar sector helps in studying the Higgs mechanism and some
Standard Model problems. We implement the correspondence between the
gauge-dependent elementary states and the non-perturbative non-abelian
gauge-invariant asymptotic states, necessary to study the non-perturbative
phenomenology of two-Higgs-doublet models. The Flavour and CP violation in
experimental data follows a hierarchical pattern, accounted by the Standard
Model. We define the Minimal Flavour Violation condition with six spurions in
effective field theories, implying Flavour and CP violation entirely dependent
on the fermion mixing matrices but independent of the fermion masses hierarchy;
it is renormalization-group invariant. We study the phenomenology of
renormalizable two-Higgs-doublet models which verify the defined condition as
consequence of a symmetry; new light physical scalars, mediating Flavour
Changing Neutral Currents, are allowed by flavour data without flavour
coefficients beyond the Standard Model; we tested the models with C++ libraries
linked by the symbolic skills of the GiNaC library and we propose more
libraries supporting a systematic search for Flavour Changing Neutral Currents.
We also map the complex to the real Poincare group representations, derive the
free Dirac equation requiring covariant localizability of the representations
and study Localization and gauge symmetries in Quantum Field Theory.
