  We show that, despite of the reparametrization symmetry of the Lagrangian
describing the interaction between a scalar field and gauge vector bosons, the
dynamics of the Higgs mechanism is really affected by the representation gauge
chosen for the Higgs field. Actually, we find that, varying the parametrization
for the two degrees of freedom of the complex scalar field, we obtain different
expressions for the Higgs mass: in its turn this entails different expressions
for the critical temperatures, ranging from zero to a maximum value, as well as
different expressions for other basic thermodynamical quantities.
