Feynman rule of a nonequilibrium process

The complete rule of the Feynman-diagram expansion of a nonequilibrium process is given by using the path-integral technique. At an initial time tI, the system is in equilibrium and is brought into the nonequilibrium state by a time-dependent Hamiltonian. All the interactions, including the initial correlation, are taken into account by a diagrammatic expansion. Besides the well-known equilibrium propagators and the conventional 2×{}2 nonequilibrium propagator matrix, the propagator becomes a 3×{}3 matrix that contains extra elements depending explicitly on tI. Both the Feynman rule of the coordinate representation and the coherent-state representation are presented. It is shown that the propagator matrix is expressed compactly by the contour representation. The classical limit is also discussed.