Consistent evolution with different time slicings in quantum gravity
Open accessAbstract
Rovelli's `quantum mechanics without time' motivates an intrinsically time-slicing-independent picture of reduced phase space quantum gravity, which may be described as `quantization after evolution'. Sufficient criteria for carrying out quantization after evolution are developed in terms of a general concept of the classical limit of quantum mechanics. If these criteria are satisfied then it is possible to have consistent unitary evolution of operators, with respect to an infinite-parameter family of time slicings (and probably all time slicings), with the correct classical limit. The criteria are particularly amenable to study in (2 + 1)-dimensional gravity, where the reduced phase space is finite dimensional.
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For (2+1)-dimensional gravity, there is evidence that one can always find operator orderings of the Hamiltonians that ensure consistent evolution.
“For (2 + 1)-dimensional gravity, on the other hand, there is evidence that one can always find operator orderings of the Hamiltonians that ensure consistent evolution [95].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [95]
The Part 3 introduction and §14 offer a non-rigorous argument for consistent evolution across time slicings in (2+1)-dimensional gravity. The Conclusion says consistent evolution could be achieved through operator orderings if quantization after evolution is equivalent to Heisenberg evolution, but establishes this only for at least an infinite-parameter family of slicings—not always or in complete generality. (LLM, conf=0.84)
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Time in quantum gravity: An hypothesis
Rovelli, C. (1991) · Physical Review D · doi:10.1103/physrevd.43.442 · Cited by 445 · see citing works
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Research works printed but not linked: 8
- Kuchař K 1992 Time and interpretations of quantum gravity 4th Canadian Conf. on General Relativity and Relativistic Astrophysics (Singapore: World Scientific)
- Crnkovic C and Witten E 1987 Three Hundred Years of Gravitation ed S W Hawking and W Israel (Cambridge: Cambridge University Press)
- Werner R F 1995 Osnabruck University Preprint RFW-95-CLS, e-Print Archive: quant-ph/9504016 · arXiv
- Guillemin and Sternberg 1984 Symplectic Techniques in Physics (Cambridge: Cambridge University Press)
- For an introduction to homotopy theory see, for example, James I M 1984 General Topology and Homotopy Theory (New York: Springer); or
- Gromov M L 1969 Math. USSR-Izvestija 3 671; 1986 Partial Differential Relations (Berlin: Springer)
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Cosgrove, R.
- Affiliations
- University of California, Davis (US)
- Corresponding author
- Cosgrove, R
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1996-05-01
- Volume
- 13
- Issue
- 5
- Pages
- 891-919
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2009246248
- Cited by
- 4
- References
- 1
- Citations by year
- 2024: 1
- FWCI
- 0.28
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy (FG0391ER40674)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- quantum gravity, time slicing, reduced phase space, unitary evolution, classical limit, Rovelli, three-dimensional gravity, timeless quantum mechanics
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