Real-Time Dimensional Reduction in Thermal Field Theory

We consider the extension of static dimensional reduction to real-time. For a scalar field theory it is shown that in the high-temperature limit this leads to an effective classical theory. Quantum corrections to the leading classical behavior are determined by an effective action which can be calculated perturbatively in the background of the classical fields. Feynman rules for (\lambda\phi^4)-theory are given and the extension to SU($N$) gauge theories is outlined.