Renormalization of the closed–time-path Green's functions in nonequilibrium statistical field theory

The problem of renormalization of the closed–time-path Green's function in nonequilibrium statistical field theory is studied. Under some reasonable assumptions on the high-energy behavior of the initial correlation functions, it is found that the same counterterms which eliminate the ultraviolet divergences in the usual field theory can also make the closed–time-path Green's functions free of ultraviolet divergences. The renormalization-group equation satisfied by the closed–time-path vertex functions is obtained and the Callan-Symanzik coefficient functions are shown to be the same as in the usual field theory.