In this paper we summarize the work done by our group in developing and applying the closed time-path Green function (CTPGF) formalism, first suggested by J. Schwinger and further elaborated by Keldysh and others. The generating functional technique and path integral representation are used to discuss the various properties of the CTPGF and to work out a practical calculation scheme. The formalism developed provides a unified framework for describing both equilibrium and nonequilibrium phenomena. It includes the ordinary quantum field theory and the classical fluctuation field theory as its limiting cases. It is well adapted to consider the symmetry breaking with either constituent or composite order parameters. The basic properties of the CTPGF are described, the two-point functions are discussed in some detail with the transport equation and the time dependent Ginzburg-Landau equation derived as illustrations. The implications of the time-reversal symmetry for stationary states are explored to derive the potential condition and to generalize the fluctuation-dissipation theorem. A system of coupled equations is derived to determine self-consistently the order parameter as well as the energy spectrum, the dissipation and the particle distribution for elementary excitations. The general formalism and the useful techniques are illustrated by applications to critical dynamics, quenched random systems, theory of nonlinear response, plasma, nuclear many-body problem and so on.

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