Invariant wave equations, propagators and generalized coherent states over de Sitter space

The invariant wave equations in the de Sitter space for spin 0 and 1/2 massive particles are constructed. The explicit solutions of these equations are obtained in the form of so-called “plane waves” without use of the separation of variables method. The connection with the generalized coherent states for the de Sitter group is established. Invariant spin 0 and 1/2 two-point functions are constructed which are the (anti)commutators of the corresponding secondly quantized fields.