Classical field dynamics of the electroweak phase transition

We investigate the thermodynamics and dynamics of the electroweak phase transition by modeling the infrared physics with classical Yang-Mills Higgs theory. We discuss the accuracy of this approach and conclude that, for quantities whose determination is dominated by the infrared, the classical method should be correct up to parametrically suppressed [i.e., $O\left(\alpha \right)]$ corrections. For a Higgs self-coupling which at the tree level corresponds to $m_H\simeq 50$ GeV, we determine the jump in the order parameter to be $\delta \phi =1.5\mathrm{gT}$, the surface tension to be $\sigma {=0.07g}^4{T}^3$, and the friction coefficient on the moving bubble wall due to infrared bosons to be $\eta \equiv {P/v}_w=0.03\mathrm{}\pm {0.004g}^6{T}^4$. We also investigate the response of the Chern-Simons number to a spatially uniform chemical potential and find that it falls off a short distance inside the bubble wall, both in equilibrium and below the equilibrium temperature.