Coarse Grainings and Irreversibility in Quantum Field Theory

In this paper we are interested in the studying coarse-graining in field theories using the language of quantum open systems. Motivated by the ideas of Calzetta and Hu on correlation histories we employ the Zwanzig projection technique to obtain evolution equations for relevant observables in self-interacting scalar field theories. Our coarse-graining operation consists in concentrating solely on the evolution of the correlation functions of degree less than $n$, a treatment which corresponds to the familiar from statistical mechanics truncation of the BBKGY hierarchy at the n-th level. We derive the equations governing the evolution of mean field and two-point functions thus identifying the terms corresponding to dissipation and noise. We discuss possible applications of our formalism, the emergence of classical behaviour and the connection to the decoherent histories framework.