Quantization of massless fields over the static Robertson-Walker space of constant negative curvature

Taking the ${\Bbb R}^1 \times H^3$ space as an example, we develop the new method of quantization of fields over symmetric spaces. We construct the quantized massless fields of an arbitrary spin over the ${\Bbb R}^1 \times H^3$ space by the resolution over the systems of "plane waves" which are solutions of the corresponding wave equations. The propagators of these fields are ${\Bbb R}^1 \times SO(3,1)$-invariant and causal. For spin 0 and 1/2 fields the propagators are obtained in the explicit form.