1995/10/31 by N. P. Landsman · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/12/003
published as Class.Quant.Grav. 12 (1995) L119-L124 · 12 pages, LaTeX; revised version corrects treatment of open minisuperspace model. No conclusions are affected by this
arxiv created 1995/11/20 · arxiv updated 2009/11/30
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 that arise in connection with this equation may be circumvented if one employs a covariant Hamiltonian method in conjunction with a recently developed, mathematically rigorous technique to quantize constrained systems using Rieffel induction. The classical constraints are cleanly separated 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 constraint that arises in any theory, parametrized or not. The new quantization method is carried through in a minisuperspace example, and is found to produce a ``wavefunction of the universe". This differs from the proposals of both Vilenkin and Hartle-Hawking for a closed FRW universe, but happens to coincide with the latter in the open case.