2+1 gravity and doubly special relativity
Open accessAbstract
It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.
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(2+1)-dimensional gravity automatically displays a deformation of the Poincaré algebra associated with doubly special relativity.
“It has recently been pointed out that (2 + 1)-dimensional gravity automatically displays such a deformation [197, 18, 126].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [126]
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Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Lorentz Invariance with an Invariant Energy Scale
Magueijo, J., & Smolin, L. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.190403 · Cited by 1,226 · see citing works
Self-citationGeneralized Lorentz invariance with an invariant energy scale
Magueijo, J., & Smolin, L. (2003) · Physical Review D · doi:10.1103/physrevd.67.044017 · Cited by 691 · see citing works
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Research works printed but not linked: 3
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Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Freidel, L., & Livine, E. R. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/6/012 · Cited by 266 · see citing works
Self-citationQuantum 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
- Freidel, L., Kowalski-Glikman, J., & Smolin, L.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- University of Wrocław (PL)
- University of Waterloo (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2004-02-06
- Volume
- 69
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2157692159
- Cited by
- 150
- References
- 3
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 3 · 2023: 2 · 2022: 5 · 2021: 4 · 2020: 3 · 2019: 3 · 2018: 4 · 2017: 10 · 2016: 2 · 2015: 6 · 2014: 8 · 2013: 8 · 2012: 6
- FWCI
- 9.58
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Centre National de la Recherche Scientifique
- 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
- three-dimensional gravity, doubly special relativity, point particles, algebra of observables, four-dimensional spacetime, quantum gravity
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