Explicit dimensional renormalization of quantum field theory in curved space-time

The dimensional renormalization of scalar and spinor field theories quantized in a conformally flat ($k=0\mathrm{}$) Robertson-Walker space-time is discussed. The theories considered are conformally invariant save explicit mass terms. All calculations are performed on the level of the canonical, Heisenberg-picture field theory, and explicit formulas derived for renormalized Heisenberg-state expectation values, such as particle production. Some solvable models are presented as illustrations of the formalism.