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Cited by 90Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Spectrum of the volume operator in quantum gravity

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Loll, R.·1996·Nuclear Physics B
DOI 10.1016/0550-3213(95)00627-3
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Crossref · 10.1016/0550-3213(95)00627-3

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  • The simple configuration variables obtained by three-dimensional smearing of connections are not gauge covariant and are unsuitable in the non-Abelian context.

    “More precisely, the simple configuration variables in (2.2) fail to be gauge covariant and are therefore unsuitable in the non-Abelian context (unless one manages to fix the gauge completely).”

    From Quantum theory of geometry: III. Non-commutativity of Riemannian structures (1998) · cites this paper as [23]

  • This representation is characterized by the fact that the holonomy is a well-defined operator in the quantum theory.

    “This representation is characterized by the fact that the holonomy is a well-defined operator in the quantum theory.”

    From Immirzi parameter in quantum general relativity (1998) · cites this paper as [6]

  • Physical and mathematical arguments indicate that this representation is relevant at the diffeomorphism-invariant and background-independent level.

    “But physical and mathematical arguments indicate that this representation is relevant at the diffeomorphism-invariant and background-independent level [6,7].”

    From Immirzi parameter in quantum general relativity (1998) · cites this paper as [6]

  • The existence of this quantization ambiguity is due to the peculiar kind of representation on which nonperturbative quantum gravity is based.

    “The existence of this quantization ambiguity is due to the peculiar kind of representation on which nonperturbative quantum gravity is based [5,6].”

    From Immirzi parameter in quantum general relativity (1998) · cites this paper as [6]

  • The computed eigenvalues agree with the numbers published by Loll.

    “Loll has computed a few of these eigenvalues in [36] using a different technique. We find agreement with the numbers published by Loll (see also [35]).”

    From Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity (1996) · cites this paper as [36]

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Authors
Loll, R.
Affiliations
Max Planck Institute for Gravitational Physics (DE)
Corresponding author
Loll, R.
ORCID
Loll, R.
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
1996-01
Volume
460
Issue
1
Pages
143-154
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/0550-3213(95)00627-3
OpenAlex
W2042427774
Cited by
90
References
11
Citations by year
2024: 1 · 2021: 1 · 2020: 1 · 2018: 1 · 2016: 1 · 2015: 2 · 2014: 3 · 2013: 1 · 2012: 2
FWCI
7.85
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • Nuclear Physics B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • Max Planck Digital Library (submittedVersion, other-oa)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
  • 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 › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
volume operator, operator spectrum, quantum gravity, spin network states, non-perturbative quantum gravity

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