A new perturbative scheme is proposed for the evaluation of the free energy density of field theories at finite temperature. The screened loop expansion takes into account exactly the phenomenon of screening in thermal propagators. The approach is tested in the N -component scalar field theory at 2-loop level and also at 3-loop in the large N limit. The perturbative series generated by the screened loop expansion shows much better numerical convergence than previous expansions generated in powers of the quartic coupling.

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, SU(2) gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar-gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find m w = 0.35(1)g 2 T in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size L 2 × L z with L = 4 − 24 and L z = 16 − 128.

A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over non-static modes leads to an effective theory containing a gauge field A a i , an adjoint Higgs field A a 0 and the fundamental Higgs field φ α . We carry out the integration in the 1-loop approximation, study renormalisation effects and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Secondly, because of the existence of well-separated thermal mass scales, A a 0 can be integrated over, and finally also φ α , leaving an effective theory of the A a i . In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom.

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