Coarse graining and decoherence in quantum field theory

We consider a λφ4 theory in Minkowski spacetime. We compute a open-quote open-quote coarse-grained effective action close-quote close-quote by integrating out the field modes with a wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients of this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. copyright 1996 The American Physical Society