The massive scalar and Dirac fields quantized on a de Sitter background geometry prove to be exactly soluble models in general-relativistic field theory. The Feynman Green's function is computed for both the scalar and Dirac fields. A dimensional regularization procedure applied in coordinate space facilitates the calculation of their respective effective Lagrangians, which describe the vacuum corrections due to closed matter loops. The model is found to be renormalizable. There is no creation of real particle pairs.