Dependence of the critical temperature on the Higgs field parametrization

Abstract

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.

Describing Sr2RuO4 superconductivity in a generalized Ginzburg–Landau theory

“…In the most transparent (for our purposes) GL formalism, after the condensations due to the U(1) SSB, the mean total free energy results as the sum of contributions from normal-conducting electrons, and from weakly-coupled and strongly-coupled Cooper pairs: (11) Note that, despite the fact that the bare masses and self-interaction coupling constants are the same for both scalar fields, the GL effective parameters a w (T ), a s (T ) are not: this depending on a different choice for the degrees of freedom, described through the scalar fields φ w , φ s , which undergone condensation [1,2,9]. In the BCS formalism this corresponds to the fact that, at lower temperatures, the electron-phonon effective interaction may be different than at higher temperatures, due to particular constitutive properties of the material considered.…”