REALLY COMPUTING NONPERTURBATIVE REAL-TIME CORRELATION-FUNCTIONS

It has been argued by Grigoriev and Rubakov that one can simulate real time processes involving baryon number nonconservation at high tempera ture using real time evolution of classical equations, and summing ove r initial conditions with a classical thermal weight. It is known that such a naive algorithm is plagued by ultraviolet divergences. In quan tum theory the divergences are regularized, but the corresponding grap hs involve the contributions from the hard momentum region and also th e new scale similar to gT comes into play. We propose a modified algor ithm which involves solving the classical equations of motion for the effective hard thermal loop Hamiltonian with an ultraviolet cutoff mu much greater than gT and integrating over initial conditions with a pr oper thermal weight. Such an algorithm should provide a determination of the infrared behavior of the real time correlation function (Q(t)Q( 0))(T) determining the baryon violation rate. Hopefully, the results o btained in this modified algorithm will be cutoff independent.