3D physics and the electroweak phase transition: Perturbation theory

Abstract

We know the Lagrangian of the SU(3)×SU(2)×U(l) standard model (SM) and, therefore, also the equilibrium thermodynamics of the quantum system with the spectrum of the SM: it is given by the functional integral $${e^{ - F/T}} = \int {D\Phi {\mkern 1mu} \exp \left[ { - \frac{1}{\hbar }\int_0^{\beta \hbar } {d\tau } \int {{d^3}} x\pounds\left( {\Phi \left( {\tau ,{\text{x}}} \right)} \right)} \right],}$$ (1) where the symbol Φ denotes generically all the fields of the SM. In a sense the problem of the electroweak (EW) phase transition thus is trivial: just calculate the above functional integral to give the free energy F and all the thermodynamics.