Renormalized field theory of critical dynamics

We formulate a Gell'Mann-Low-type renormalization group approach to the critical dynamics of stochastic models described by Langevin or Fokker-Planck equations including mode-coupling terms.Dynamical correlation and response functions are expressed in terms of path integrals, which are investigated by well-known methods of renormalized perturbation theory.Dynamical scaling laws and relations between static and dynamic critical exponents are derived. The leading temperature-dependence of correlation and response functions is obtained from the Kadanoff-Wilson short-distance expansion. We also consider corrections to dynamic scaling which are due to a finite lattice constant.