  The linear and nonlinear processes in ferromagnetic films at low temperatures
T<< Tc are studied in a microscopic theory. Both the long-range magnetic
dipole-dipole and the Heisenberg exchange interactions to nearest and
next-nearest neighbors are included. The results obtained for the linearized
spin-wave spectrum are compared with previous macroscopic theories. For
ultrathin films (or for large wave vectors) the microscopic theory provides
important corrections. The nonlinear dynamics of the spin waves are studied
through a finite-temperature perturbation theory based on Feynman diagrams. We
obtain explicit results for the energy shift and damping (or reciprocal
lifetime) of the dipole-exchange spin waves due to all possible three-magnon
and four-magnon processes involving combinations of the surface and quantized
bulk spin waves at low temperatures. To investigate different dipole
interaction strengths (relative to the exchange) numerical results are
presented using parameters for Fe, EuO, and GdCl3.
