Remarks on the issue of time and complex numbers in canonical quantum gravity

Upon using some special example in the homogeneous cosmological model we develop the idea that, as a result of the arbitrariness of the factor ordering in the Wheeler-DeWitt equation, gauge phases cannot, in general, be completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in the WDW equation depending on the factor ordering. Taking this equation for granted, we can obtain WKB complex solutions and, therefore, should be able to derive a semiclassical time parameter for the Schrödinger equation corresponding to matter fields in a given classical curved space.