  Critical dynamics in film geometry is analyzed within the field-theoretical
approach. In particular we consider the case of purely relaxational dynamics
(Model A) and Dirichlet boundary conditions, corresponding to the so-called
ordinary surface universality class on both confining boundaries. The general
scaling properties for the linear response and correlation functions and for
dynamic Casimir forces are discussed. Within the Gaussian approximation we
determine the analytic expressions for the associated universal scaling
functions and study quantitatively in detail their qualitative features as well
as their various limiting behaviors close to the bulk critical point. In
addition we consider the effects of time-dependent fields on the
fluctuation-induced dynamic Casimir force and determine analytically the
corresponding universal scaling functions and their asymptotic behaviors for
two specific instances of instantaneous perturbations. The universal aspects of
nonlinear relaxation from an initially ordered state are also discussed
emphasizing the different crossovers that occur during this evolution. The
model considered is relevant to the critical dynamics of actual uniaxial
ferromagnetic films with symmetry-preserving conditions at the confining
surfaces and for Monte Carlo simulations of spin system with Glauber dynamics
and free boundary conditions.
