We derive an effective dimensionally reduced theory for the Standard Model augmented by a real singlet scalar. We treat the singlet as a superheavy field and integrate it out, leaving an effective theory involving only the Higgs and SU(2)(L) x U(1)(y) gauge fields, identical to the one studied previously for the Standard Model. This opens up the possibility of efficiently computing the order and strength of the electroweak phase transition, numerically and nonperturbatively, in this extension of the Standard Model. Understanding the phase diagram is crucial for models of electroweak baryogenesis and for studying the production of gravitational waves at thermal phase transitions.

We study the phase space structure of exact quantum Wightman functions in spatially homogeneous, temporally varying systems. In addition to the usual mass shells, the Wightman functions display additional coherence shells around zero frequency k(0) = 0, which carry the information of the local quantum coherence of particle-antiparticle pairs. We find also other structures, which encode non-local correlations in time, and discuss their role and decoherence. We give a simple derivation of the cQPA formalism, a set of quantum transport equations, that can be used to study interacting systems including the local quantum coherence. We compute quantum currents created by a temporal change in a particle's mass, comparing the exact Wightman function approach, the cQPA and the semiclassical methods. We find that the semiclassical approximation, which is fully encompassed by the cQPA, works surprisingly well even for very sharp temporal features. This is encouraging for the application of semiclassical methods in electroweak baryogenesis with strong phase transitions.