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Cited by 106Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Probing quantum gravity through exactly soluble midi-superspaces I

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Ashtekar, A., Pierri, M.·1996·Journal of Mathematical Physics
DOI 10.1063/1.531774
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Abstract

It is well-known that the Einstein-Rosen solutions to the 3+1- dimensional vacuum Einstein’s equations are in one to one correspondence with solutions of 2+1-dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity.

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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 [32]

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Research works printed but not linked: 18

  1. [1][1] Conceptual Problems of Quantum Gravity, eds A. Ashtekar and J. Stachel (Birkhäuser, Boston, 1991); C.J. Isham, in The Proceedings of the 1992 NATO advanced study institute on Recent Problems in Mathematical Physics; K. Kuchař, in The Proceedings of the 4th Canadian conference on General Relativ- ity and Relativistic Astrophysics, eds G. Kunstatter, D. Vincent and J. Williams (World Scientific, Singapore, 1992).
  2. [2][2] C. W. Misner, In Magic Without Magic: John Archibald Wheeler, edited by J. Klauder (Freeman, San Francisco, 1972); M. Ryan, Hamiltonian Cosmology, (Springer-Verlag, Berlin, 1972); A. Ashtekar, R.S. Tate and C. Uggla, Int. J. Theo. Physics, D2, 15 (1993).
  3. [3][3] Carlip, In: Knots and Quantum Gravity, ed J. Baez (Clarendon Press, Oxford, 1994); J. Korean Phys. Soc. (Proc. Suppl.), 28, S447 (1995).
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  7. [8][8] A. Ashtekar and M. Varadarajan, Phys. Rev. D 40, 4944 (1994).
  8. [9][9] M. Varadarajan, Phys. Rev. D 52, 2020 (1995).
  9. [11][11] E. Witten, Nucl. Phys. B311, 46 (1988); A. Ashtekar, V. Husain, C. Rovelli, J. Samuel and L. Smolin, Class. & Grav. 6, L185 (1989).
  10. [12][12] J. Glimm and A. Jaffe, Quantum Physics (Springer-Verlag, New York, 1987).
  11. [13][13] A. Ashtekar, J. Bicak and B.S. Schmidt, preprint CGPC-96/5-1.
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  17. [20][20] D. Korotkin and H. Nicolai, pre-print hep-th/9605144. · arXiv
  18. [22][22] S. Frettelli, C. Kozameh, E.T. Newman, C. Rovelli and R.S. Tate, pre-print gr-qc/9603061. 28 http://arxiv.org/abs/hep-th/9605144 http://arxiv.org/abs/gr-qc/9603061 · arXiv

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Authors
Ashtekar, A., & Pierri, M.
Affiliations
Pennsylvania State University (US)
ORCID
Ashtekar, A.
Venue
Journal of Mathematical Physics
Publisher
AIP Publishing
Published
1996-12-01
Volume
37
Issue
12
Pages
6250-6270
ISSN
  • 0022-2488 (ISSN-L)
  • 1089-7658
DOI
10.1063/1.531774
OpenAlex
W2002937364
Cited by
106
References
2
Citations by year
2025: 16 · 2024: 1 · 2022: 3 · 2021: 2 · 2020: 1 · 2017: 1 · 2016: 1 · 2014: 2 · 2013: 1
FWCI
5.07
Type
journal article
Language
en
Open access
Locations
  • Journal of Mathematical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation
  • Pennsylvania State 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 › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
quantum gravity, scalar field, regularization, exactly solvable models

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