Exact CTP renormalization group equation for the coarse-grained effective action

We consider a scalar field theory in Minkowski spacetime and define a coarse-grained closed time path (CTP) effective action by integrating quantum fluctuations of wavelengths shorter than a critical value. We derive an exact CTP renormalization group equation for the dependence of the effective action on the coarse-graining scale. We solve this equation using a derivative expansion approach. Explicit calculation is performed for the lambda phi(4) theory. We discuss the relevance of the CTP average action in the study of nonequilibrium aspects of phase transitions in quantum field theory.