Reaction diffusion with initially separated reactants: Functional integral approach

A method based on the Feynman-Kac formula is suggested to analyze the solutions of the $A+B\to C$ reaction-diffusion system with initially separated reactants. It enables us to reproduce and improve earlier results which were based on empirical approximations. We also roughly estimate an upper time limit for this approach to be valid. It is possible that this limit is the applicability limit for the mean-field approach.