Quantum aspects of classical and statistical fields

Abstract

A generating functional for a classical system described by coordinates satisfying nonlinear equations of motion is constructed in terms of which any functional of the system's phase-space trajectory may be expressed. Statistical behavior of the system arising from either random initial conditions or random stirring forces may be handled simply within this theory. The analogy with Feynman's action-integral formalism of quantum theory provides an alternative approach to the operator methods recently developed by Martin, Siggia, and Rose. The connection with the earlier work of Onsager, Machlup, and Graham is also pointed out.