Constraints in Quantum Geometrodynamics

Journal Article · Wed Jan 25 04:00:00 EST 2012 · International Journal of Modern Physics A

DOI:https://doi.org/10.1142/s0217751x04017008· OSTI ID:824475

Gentle, Adrian P. ^[1]; George, Nathan D. ^[2]; Kheyfets, Arjady ^[3]; Miller, Warner A. ^[4]

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1. Department of Mathematics, University of Southern Indiana, Evansville, IN 47712, USA; Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
2. DAMTP, University of Cambridge, Cambridge CB3 0WA, UK; Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
4. Department of Physics, Florida Atlantic University, Boca Raton, FL 33431, USA; Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 824475
• Report Number(s): LA-UR-03-0782
• Journal Information: International Journal of Modern Physics A, Journal Name: International Journal of Modern Physics A Journal Issue: 10 Vol. 19; ISSN 0217-751X
• Publisher: World Scientific
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS