Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-10-17
Class.Quant.Grav. 12 (1995) L119-L124
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, LaTeX; revised version corrects treatment of open minisuperspace model. No conclusions are affected by this
Scientific paper
10.1088/0264-9381/12/12/003
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.
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