A SELF-CONSISTENT STUDY OF THE PHASE-TRANSITION IN THE SCALAR ELECTROWEAK THEORY AT FINITE-TEMPERATURE

We propose the study of tile phase transition ill the scalar electrowe ak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbat ive blockspin transformation, and ii) either further real space renorm alization group transformations, or solution of gap equations, for til e 3d lattice theory. A gap equation can be obtained by using tile Peie rls inequality to find the best quadratic approximation to the 3d acti on. This Method avoids the lack of self consistency of tile usual trea tments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be use d ill computer simulations.