  We consider quantum corrections to classical real time correlation functions
at finite temperature. We derive a semi-classical expansion in powers of
$\hbar$ with coefficients including all orders in the coupling constant. We
give explicit expressions up to order $\hbar^2$. We restrict ourselves to a
scalar theory. This method, if extended to gauge theories, might be used to
compute quantum corrections to the high temperature baryon number violation
rate in the Standard Model.

High Energy Physics - Theory;High Energy Physics - Phenomenology