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The aim of this paper is two-fold: in probing the statistical mechanicalproperties of interacting quantum fields, and in providing a field theoreticaljustification for a stochastic source term in the Boltzmann equation. We startwith the formulation of quantum field theory in terms of the Schwinger - Dysonequations for the correlation functions, which we describe by aclosed-time-path master ($n = \infty PI$) effective action. When the hierarchyis truncated, one obtains the ordinary closed-system of correlation functionsup to a certain order, and from the nPI effective action, a set oftime-reversal invariant equations of motion. But when the effect of the higherorder correlation functions is included (through e.g., causal factorization--molecular chaos -- conditions, which we call 'slaving'), in the form of acorrelation noise, the dynamics of the lower order correlations showsdissipative features, as familiar in the field-theory version of Boltzmannequation. We show that fluctuation-dissipation relations exist for sucheffectively open systems, and use them to show that such a stochastic term,which explicitly introduces quantum fluctuations on the lower order correlationfunctions, necessarily accompanies the dissipative term, thus leading to aBoltzmann-Langevin equation which depicts both the dissipative and stochasticdynamics of correlation functions in quantum field theory.Comment: LATEX, 30 pages, no figure

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation