Enforcing the Wheeler-DeWitt constraint the easy way
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The author proves that the Wheeler-DeWitt symmetry must be gauge-fixed in canonical inner products. When this is done every functional integral represents the expectation value of an invariant operator in the presence of an invariant state. A corollary is that certain minisuperspace models are devoid of quantum phenomena.
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The inner product on the space of solutions of the Wheeler-DeWitt equation must be gauge-fixed, and little is understood about the resulting Hilbert space.
“Further complications come from the fact that the inner product on the space of solutions of the Wheeler-DeWitt equation must be gauge-fixed [282, 144]; again, little is understood about the resulting Hilbert space.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [282]
The discussion of formula (13c) says that the inner product of invariant states must be gauge-fixed, directly supporting the first part of the claim. The paper discusses unresolved questions about observables and physical time, but does not say that little is understood about the resulting Hilbert space. (LLM, conf=0.85)
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Research works printed but not linked: 3
- Kuchaf K 1991 Conceptual Probkms of Quantum Gravity ed A Ashtekar and J Slachel P m . 4th Canadian Conference on Genera/ Relafivig and Relotivkic Astrophysics (Boslon 1591) (Singapore: World Scientific)
- Isham C J 1992 Canonical quantum gravity and the problem of time Impend CoI/ege preprint Tpi91-92N
- Rubio J and Woodard R P, Reduced Hamiltonians University of Florida preprint in prepareation
Cited by
Sorted by citations
Quantum gravity and Regge calculus
Immirzi, G. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00354-x · Cited by 287 · see citing works
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
Carlip, S. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acceb4 · Cited by 41 · see citing works
- Authors
- Woodard, R. P.
- Affiliations
- University of Florida (US)
- Corresponding author
- Woodard, R P
- ORCID
- Woodard, R P
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1993-03-01
- Volume
- 10
- Issue
- 3
- Pages
- 483-496
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2061692451
- Cited by
- 64
- References
- 0
- Citations by year
- 2026: 1 · 2025: 15 · 2024: 3 · 2023: 4 · 2022: 4 · 2021: 4 · 2020: 1 · 2018: 1 · 2017: 2 · 2015: 1 · 2012: 3
- FWCI
- 1.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Funders
- U.S. Department of Energy (DE-AC02-76ER03130, DE-AC02-)
- Aspen Center for Physics
- 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
- Wheeler-DeWitt equation, constraint quantization, gauge fixing, path integral, invariant operators, invariant states, minisuperspace model, quantum gravity
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