Inhomogeneous Field Configurations and the Electroweak Phase Transition

We investigate the effects of inhomogeneous scalar field configurations on the electroweak phase transition. For this purpose we calculate the leading perturbative correction to the wave function correction term $Z(\vph,T)$, i.e., the kinetic term in the effective action, for the electroweak Standard Model at finite temperature and the top quark self--mass. Our finding for the fermionic contribution to $Z(\vph,T)$ is infra--red finite and disagrees with other recent results. In general, neither the order of the phase transition nor the temperature at which it occurs change, once $Z(\vph,T)$ is included. But a non--vanishing, positive (negative) $Z(\vph,T)$ enhances (decreases) the critical droplet surface tension and the strength of the phase transition. We find that in the range of parameter space, which allows for a first--order phase transition, the wave function correction term is negative --- indicating a weaker phase transition --- and especially for small field values so large that perturbation theory becomes unreliable.