Remarks on the issue of time and complex numbers in canonical quantum   gravity
  We develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in WDW equation depending of the factor ordering. Taking this equation for granted we can obtain WKB complex solutions and, therefore, we should be able to derive a semiclassical time parameter for the Schroedinger equation corresponding to matter fields in a given classical curved space. 
Jose-Luis Rosales