Conditional probabilities with Dirac observables and the problem of time in quantum gravity

Journal Article · Sun Feb 15 00:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.041501· OSTI ID:21259962

Gambini, Rodolfo; Torterolo, Sebastian ^[1]; Porto, Rafael A ^[2]; Pullin, Jorge ^[3]

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1. Instituto de Fisica, Facultad de Ciencias, Igua 4225, esq. Mataojo, Montevideo (Uruguay)
2. Department of Physics, University of California, Santa Barbara, California 93106 (United States)
3. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001 (United States)

We combine the 'evolving constants' approach to the construction of observables in canonical quantum gravity with the Page-Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the objections levied by Kuchar against the latter formalism. The construction is formulated entirely in terms of Dirac observables, avoiding in all cases the physical observation of quantities that do not belong in the physical Hilbert space. We work out explicitly the example of the parametrized particle, including the calculation of the propagator. The resulting theory also predicts a fundamental mechanism of decoherence.

• OSTI ID: 21259962
• Journal Information: Physical Review. D, Particles Fields, Vol. 79, Issue 4; Other Information: DOI: 10.1103/PhysRevD.79.041501; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC OPERATORS
HILBERT SPACE
PROBABILITY
PROPAGATOR
QUANTUM DECOHERENCE
QUANTUM GRAVITY
QUANTUM MECHANICS