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Cited by 68Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

The geometry of quantum spin networks

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Borissov, Roumen, Major, Seth, Smolin, Lee·1996·Classical and Quantum Gravity
DOI 10.1088/0264-9381/13/12/009
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Abstract

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The eigenstates are expressed in terms of q-deformed spin networks. The q-deformation breaks some of the degeneracy of the volume operator so that trivalent spin-networks have non-zero volume. These computations are facilitated by use of a technique based on the recoupling theory of SU(2)_q, which simplifies the construction of these and other operators through diffeomorphism invariant regularization procedures.

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  • Quantum GR does not admit a rigorous finite version as quantum BF, at least as far as we can presently see, even if one attempts to replace SU(2) with quantum SU(2) in GR.

    “Thus, quantum GR does not admit a rigorous finite version as quantum BF, at least as far as we can presently see, even if one attempts to replace SU (2) with quantum SU (2) in GR [65].”

    From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [65]

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Research works printed but not linked: 16

  1. [2][2] M. Atiyah, Topological Quantum Field Theory Publ. Math. IHES 68 (1989) 175186; The Geometry and Physics of Knots, Lezione Lincee (Cambridge University Press,1990). -
  2. [5][5] L. Smolin, Modern Physics Letters A 4 (1989) 1091-1112. -
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  4. [11][11] R. J. Lawrence, in Quantum Topology (World Scientific,1993) , p.191 and An introduction to topological quantum field theory preprint (1995). -
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  6. [19][19] L. Crane, Clocks and Categories, is quantum gravity algebraic? JMP Nov. (1995). Categorical Physics , in Knot theory and quantum gravity ed. J. Baez, -(Oxford University Press); -
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  13. [42][42] A. Ashtekar, Polymer Geometry at Planck Scale and Quanrum Einstein Equations , preprint CGPG-95/11-1. -
  14. [43][43] S. Major, 'A graph Invariant for Chern-Simons Theory' preprint in preparation. -
  15. [44][44] T. Thiemann, preprints gr-qc/9511057, CGPG-95/11-4, HUTMP-95/B-348; grqc/9511049, CGPG-95/11-3, HUTMP-95/B-347. - · arXiv
  16. [46][46] T. Jacobson, Phys. Rev. Lett. 75 (1995) 1260-1263, gr-qc/9504004. - · arXiv

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Related

Authors
Borissov, R., Major, S., & Smolin, L.
Affiliations
Pennsylvania State University (US)
ORCID
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
1996-12-01
Volume
13
Issue
12
Pages
3183-3195
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/13/12/009
OpenAlex
W2041385653
Cited by
68
References
51
Citations by year
2024: 3 · 2023: 2 · 2022: 1 · 2021: 1 · 2020: 1 · 2018: 2 · 2017: 1 · 2016: 3 · 2015: 5 · 2014: 2 · 2013: 1 · 2012: 2
FWCI
5.37
Type
journal article
Language
en
Open access
Locations
  • Classical and Quantum Gravity (publishedVersion)
  • arXiv (Cornell University) (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 › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
quantum spin networks, loop quantum gravity, q-deformation, area operator, volume operator, diffeomorphism invariance, combinatorial geometry, eigenstates

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