Quantization of fields over de Sitter space by the method of generalized coherent states

A system of generalized coherent states (CS) for the de Sitter (dS) group obeying the Klein-Gordon equation and corresponding to the massive spin-0 particles over the dS space is considered. This allows us to construct the quantized scalar field by resolution over these CS; the corresponding propagator is computed by the method of analytic continuation to the complex dS space and coincides with expressions obtained previously by other methods. Considering the case of spin-1/2, we establish the connection of the invariant Dirac equation over the dS space with irreducible representations of the dS group. The set of solutions of this equation is obtained in the form of the product of two different systems of generalized CS for the dS group. Using these solutions the quantized Dirac field over dS space is constructed and its propagator is found. It is a result of the action of some dS invariant spinor operator onto the spin-0 propagator with an imaginary shift of a mass. We show that the constructed propagators possess the dS invariance and causality properties. (author)