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

Dependence of the critical temperature on the Higgs field reparametrization