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 and solve it using a derivative expansion approach. Explicit calculation is performed for the λφ4 theory. We discuss the relevance of the CTP average action in the study of non-equilibrium aspects ∗Electronic address: [email protected] †Electronic address: [email protected] 1 of phase transitions in quantum field theory.