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Cited by 102Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Clock and category: Is quantum gravity algebraic?

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Crane, Louis·1995·Journal of Mathematical Physics
DOI 10.1063/1.531240
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Abstract

We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories. The algebraic structures are related to ideas about the reinterpretation of quantum mechanics in a general relativistic context.

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  • The construction was generalized to four dimensions by Crane and Yetter, giving a discrete topological field theory corresponding in the continuum to BF theory and an invariant of 4-manifolds.

    “This construction was generalized to the four-dimensional case by Crane and Yetter [25,26], giving a discrete topological field theory corresponding in the continuum to BF theory [57] and an invariant of 4-manifolds.”

    From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [57]

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Research works printed but not linked: 8

  1. [1][1] M. Atiyah , Topological Quantum Field Theory , Cambridge University Press , 1990.
  2. [7][7] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, 1971.
  3. [15][15] G. Kuperberg , Involutory Hopf Algebras and Three-manifold Invariants, Int. J. Math. p41-61, 1989 See also : Non-Involutory Hopf algebras and 3-Manifold Invariants, preprint, U. of Chicago math department
  4. [20][20] L. Crane and D. Yetter, On Algebraic Structures Implicit in Topological Quantum field Theories, submitted to CMP, Hepth preprint 9412025
  5. [21][21] M. Kapranov and V. Voevodsky, Braided Monoidal 2-Categories, 2Vector Spaces and Zamolodchikov's Tetrahedra Equation, preprint.
  6. [22][22] D.N. Yetter, Categorical linear algebra-A setting for questions from physics and low-dimensional topology, preprint, 1993.
  7. [25][25] M. Fukama, S. Hosong, and H. Kawai , Lattice Topological Field Theory , preprint, 1993
  8. [28][28] L. Crane and D. Yetter, A Categorical Construction of 4D-TQFTs, in Quantum Topology, World Scientific, 1993 L. Kauffman, ed.

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Authors
Crane, L.
Affiliations
Kansas State University (US)
Corresponding author
Crane, Louis
Venue
Journal of Mathematical Physics
Publisher
AIP Publishing
Published
1995-11-01
Volume
36
Issue
11
Pages
6180-6193
ISSN
  • 0022-2488 (ISSN-L)
  • 1089-7658
DOI
10.1063/1.531240
OpenAlex
W2053589237
Cited by
102
References
20
Citations by year
2026: 1 · 2024: 1 · 2023: 5 · 2022: 4 · 2020: 2 · 2019: 1 · 2018: 1 · 2017: 9 · 2016: 4 · 2015: 2 · 2014: 2 · 2013: 3
FWCI
6.14
Type
journal article
Language
en
Open access
Locations
  • Journal of Mathematical Physics (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 gravity, discrete spacetime, topological field theory, algebraic structures, general relativity

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