Functional and graphical methods for classical statistical dynamics. I. A formulation of the Martin–Siggia–Rose method

摘要: A formulation of the Martin–Siggia–Rose (MSR) method for describing statistical dynamics classical systems is presented. The present very similar in structure to original MSR “operator” formalism and different from alternative functional integral Janssen, de Dominicis, Peliti, others. need imposing certain boundary conditions formalism, as pointed out by Deker, clarified. basic results this paper include: a construction way that demonstrates its internal consistency; definition whose derivatives give all correlation functions response an ensemble mechanical systems; graphical expression functions; Legendre transform resulting vertex derivation appropriate Dyson equation. applicable with highly non-Gaussian statistics, including particles described terms particle density single-particle phase space. In paper, we consider only case ensembles coordinates are continuous time evolution deterministic first order differential equations local time. easily extended governed stochastic spin systems.