NONEQUILIBRIUM STATISTICAL FIELD THEORY AND CRITICAL DYNAMICS (I): GENERALIZED LANGEVIN EQUATION

Starting from the equations satisfied by the vertex functions on the closed time path, we derived the generalized Langevin equations for the order parameters and the conserved variables. The proper form of the equations for the conserved variables, including automatically the mode coupling terms, was determined from the Ward-Taka-hashi identities and the linear response theory. All existing dynamic models were recovered by assuming the corresponding symmetry properties of the system. The whole theoretical framework is also applicable for describing the systems near steady states far from equilibrium.