UNITARY VERSUS COVARIANT QUANTIZATION OF PARAMETRIZED THEORIES AND NORMAL ORDERING IN MINISUPERSPACE

A calculation of the one-loop approximation to wave functions of parametrized theories (such as the point particle in the stringy formalism and quantum cosmology in minisuperspace) is considered in the unitary gauge. We show that in these theories the ghost determinant is not cancelled by the contribution of unphysical momenta as could be thought, but instead it provides the well-known WKB preexponential factor 1/square-root p. By taking this contribution into account we derive a normal ordering of the Wheeler-DeWitt minisuperspace equation for a specific choice of the path integral measure.