On the metric operator for quantum cylindrical waves
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Every (one-polarization) cylindrical wave solution of vacuum general relativity is completely determined by a corresponding axisymmetric solution to the free scalar wave equation on an auxiliary (2 + 1)-dimensional flat spacetime. The physical metric at radius R is determined by the energy, ( R ), of the scalar field in a box (in the flat spacetime) of radius R . In a recent work, among other important results, Ashtekar and Pierri have introduced a strategy to study the quantum geometry in this system, through a regularized quantum counterpart of ( R ). We show that this regularized object is a densely defined symmetric operator, thereby correcting an error in their proof of this result. We argue that it admits a self-adjoint extension and show that the operator, unlike its classical counterpart, is not positive.
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Work on circularly symmetric midi-superspace models has led to unexpected bounds on the Hamiltonian.
“Certain matter couplings in supergravity have been studied [104, 196], and work on circularly symmetric “midi-superspace models” has led to some surprising results, including unexpected bounds on the Hamiltonian [27, 32, 137, 53, 265, 224].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [265]
The discussion (p. 12) identifies the cylindrical-wave model as a midisuperspace and says its regulated metric operator can be viewed as a spatially smeared Hamiltonian. But it treats whether that operator has a lower bound as an open question; this paper does not establish the claimed Hamiltonian bound. (LLM, conf=0.85)
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Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · see citing works
Quantum theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852 · see citing works
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Research works printed but not linked: 12
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Quantum geometry of isolated horizons and black hole entropy
Ashtekar, A., Baez, J. C., & Krasnov, K. (2000) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2000.v4.n1.a1 · Cited by 580 · 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
- Authors
- Varadarajan, M.
- Affiliations
- Raman Research Institute (IN)
- Corresponding author
- Varadarajan, Madhavan
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1999-12-13
- Volume
- 17
- Issue
- 1
- Pages
- 189-199
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2029649621
- Cited by
- 18
- References
- 2
- Citations by year
- 2022: 1 · 2021: 1 · 2020: 1
- FWCI
- 1.02
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- cylindrical waves, metric operator, quantum geometry, scalar wave equation, flat spacetime, self-adjoint extensions, positivity of operators
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