  We consider a $\lambda \phi^4$ theory in Minkowski spacetime. We compute a
"coarse grained effective action" by integrating out the field modes with
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 DeSitter spacetime. We show that the
decoherence is effective as long as the critical wavelength is taken to be not
shorter than the Hubble radius.
