AGAINST THE WHEELER-DEWITT EQUATION

The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties th at arise in connection with this equation may be circumvented if one e mploys a covariant Hamiltonian method in conjunction with a recently d eveloped, mathematically rigorous technique to quantize constrained sy stems using Rieffel induction. The classical constraints are cleanly s eparated into four components of a covariant momentum map coming from the diffeomorphism group of spacetime, each of which is linear in the canonical momenta, plus a single finite-dimensional quadratic constrai nt that arises in any theory, parametrized or not. The new quantizatio n method is carried through in a minisuperspace example, and is found to produce a 'wavefunction of the universe'. This differs from the pro posals of both Vilenkin and Hartle-Hawking for a closed FRW universe, but happens to coincide with the latter in the open case.