  We analyse two principal approaches to the quantization of physical models
worked out to date. There are the Faddeev-Popov "heuristic" approach, based on
fixing a gauge in the FP path integrals formalism, and the "fundamental"
approach by Dirac based on the constraint-shell reduction of Hamiltonians with
deleting unphysical variables. The relativistic invariant FP "heuristic"
approach deals with the enough small class of problems associated with
S-matrices squared taking on-shell of quantum fields. On the other hand, the
"fundamental" quantization approach by Dirac involves the manifest relativistic
covariance of quantum fields survived the constraint-shell reduction of
Hamiltonians. This allows to apply this approach for the more broad class of
problems than studying S-matrices. Researches about various bound states in QED
and QCD are patterns of such applications. In the present study, with the
example of the Dirac "fundamental" quantization of the Minkowskian non-Abelian
Higgs model (us studied in its historical retrospective), we make sure in
obvious advantages of this quantization approach. The arguments in favour of
the Dirac fundamental quantization of physical model as a way of Einstein and
Galilei relativity in modern physic will be presented.
