Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-02-12
Int.J.Mod.Phys. A19 (2004) 1609-1638
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
36 pages, no figures, submitted to IJMPA, Rewording, Fixed Typos
Scientific paper
10.1142/S0217751X04017008
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.
Gentle Adrian P.
George Nathan D.
Kheyfets Arkady
Miller Warner A.
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