THE SEARCH FOR NEW REPRESENTATIONS OF THE WHEELER-DEWITT EQUATION USING THE 1ST-ORDER FORMALISM

We obtain all possible representations of the Wheeler DeWitt equation that may arise from the development of the first-order formalism for t he quantization of gravity. They are the usual one, the modified extri nsic curvature representation and the intrisic and extrinsic time repr esentations, which arise naturally in this formalism. We show that in the intrinsic time representation the factor-ordering problem is restr icted to the pair consisting of the determinant of the metric of the s pacelike hypersurfaces and its canonical momentum. Contrary to what wa s suggested in an earlier paper, no new representations can be obtaine d in this formalism or by considering actions differing by a total div ergence.