Dynamical viscosity of nucleating bubbles

We study the viscosity corrections to the growth rate of nucleating bubbles in a slightly supercooled first order phase transition. We propose a microscopic approach that leads to the nonequilibrium equation of motion of the coordinate that describes small departures from the critical bubble and allows to extract the growth rate consistently in a weak coupling expansion and in the thin wall limit. In 3 + 1 dimensions we recognize model independent long-wavelength hydrodynamic fluctuations that describe surface waves. The coupling of this coordinate to these hydrodynamic modes results in the largest contribution to the viscosity corrections to the growth rate. The growth rate was calculated for a φ4 scalar field theory to lowest order in the coupling constant.