  We search a canonical basis of Dirac's observables for the classical
non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal
bundle with a complex doublet of Higgs fields and with the fermions in a given
representation of SU(2). Since each one of the three Gauss law first class
constraints can be solved either in the corresponding longitudinal electric
field or in the corresponding Higgs momentum, we get a priori eight disjoint
phases of solutions of the model. The only two phases with SU(2) covariance are
the SU(2) phase with massless SU(2) fields and the Higgs phase with massive
SU(2) fields. The Dirac observables and the reduced physical (local)
Hamiltonian and (nonlocal) Lagrangian of the Higgs phase are evaluated: the
main result is the nonanalyticity in the SU(2) coupling constant, or
equivalently in the sum of the residual Higgs field and of the mass of the
SU(2) fields. Some comments on the function spaces needed for the gauge fields
are made.
