Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation - art. no. 025012

The aim of this paper is twofold. to probe the statistical mechanical prope rties of interacting quantum fields, and to provide a field theoretical jus tification for a stochastic source term in the Boltzmann equation. We start with the formulation of quantum field theory in terms of the set of Schwin ger-Dyson equations for the correlation functions, which we describe by a c losed-time-path master (n = infinity PI) effective action. When the hierarc hy is simply truncated to a certain order, one obtains the usual closed sys tem of correlation functions up to that order, and from the nPI effective a ction, a set of time-reversal invariant equations of motion. (This is the D yson equation, the quantum field theoretical parallel of the collisionless Boltzmann equation.) But when the effect of the higher order correlation fu nctions is included through a causal factorization condition (such as the m olecular chaos assumption in Boltzmann's theory) called staving, the dynami cs of the lower order correlations shows dissipative features, as familiar in the usual (dissipative yet noiseless) Boltzmann equation, the field-theo retical Version of which bring the dissipative Dyson equations. We show tha t a fluctuation-dissipation relation should exist for such effectively open systems, and use this fact to show that a stochastic term, which explicitl y introduces quantum fluctuations in the lower order correlation functions, necessarily accompanies the dissipative term. This leads to a stochastic D yson equation, which is the quantum held theoretic parallel of the classica l Boltzmann-Langevin equation, encompassing both the dissipative and stocha stic dynamics of correlation functions.