Particles as Wilson lines of the gravitational field
Open accessAbstract
Since the work of Mac-Dowell-Mansouri it is well known that gravity can be written as a gauge theory for the de Sitter group. In this paper we consider the coupling of this theory to the simplest gauge invariant observables that is, Wilson lines. The dynamics of these Wilson lines is shown to reproduce exactly the dynamics of relativistic particles coupled to gravity, the gauge charges carried by Wilson lines being the mass and spin of the particles. Insertion of Wilson lines breaks in a controlled manner the diffeomorphism symmetry of the theory and the gauge degree of freedom are transmuted to particles degree of freedom.
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One-dimensional particles can be introduced in four-dimensional BF theory and gravity.
“It is also possible to introduce one-dimensional particles in four-dimensional BF theory and gravity as shown in [180].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [180]
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Geometry, Topology and Physics
Nakahara, M. (1990) · doi:10.1887/0750306068 · Cited by 1,620 · see citing works
Spinning test-particles in general relativity. I
Papapetrou, A. (1951) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1951.0200 · Cited by 1,107 · see citing works
Unified Geometric Theory of Gravity and Supergravity
MacDowell, S. W., & Mansouri, F. (1977) · Physical Review Letters · doi:10.1103/physrevlett.38.739 · Cited by 737 · see citing works
3D Quantum Gravity and Effective Noncommutative Quantum Field Theory
Freidel, L., & Livine, E. R. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.221301 · Cited by 298 · see citing works
Self-citationPonzano–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, torsion, parity violation, and all that
Freidel, L., Minić, D., & Takeuchi, T. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.104002 · Cited by 203 · see citing works
Self-citationPhysical effects of the Immirzi parameter in loop quantum gravity
Pérez, A., & Carlo Rovelli, C. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.044013 · Cited by 195 · see citing works
Unified Geometric Theory of Gravity and Supergravity
MacDowell, S. W., & Mansouri, F. (1977) · Physical Review Letters · doi:10.1103/physrevlett.38.1376 · Cited by 180 · see citing works
Quantization of symplectic orbits of compact Lie groups by means of the functional integral
Alekseev, A., Faddeev, L. D., & Shatashvili, S. L. (1988) · Journal of Geometry and Physics · doi:10.1016/0393-0440(88)90031-9 · Cited by 169 · see citing works
Quantum gravity in terms of topological observablesPreprint
Freidel, L., & Starodubtsev, A. N. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0501191 · Cited by 132 · see citing works
Self-citationOn spin and (quantum) gravity in 2 + 1 dimensions
Gerbert, P. D. S. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90288-o · Cited by 128 · see citing works
Gauge Symmetries and Fibre Bundles
Balachandran, A. P., Marmo, G., Skagerstam, B.-S., & Stern, A. (1983) · Springer eBooks · doi:10.1007/3-540-12724-0 · Cited by 112 · see citing works
General relativity with a topological phase: an action principlePreprint
Smolin, L., & Starodubtsev, A. N. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0311163 · Cited by 42 · see citing works
Self-citationQuantization of strings and branes coupled to BF theory
Baez, J. C., & Pérez, A. (2007) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2007.v11.n3.a4 · Cited by 34 · see citing works
Doubly Special Relativity: facts and prospectsPreprint
Kowalski-Glikman, J. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0603022 · Cited by 29 · see citing works
Self-citationA Note on Parity Violation and the Immirzi ParameterPreprint
Randono, A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0510001 · Cited by 18 · see citing works
Quantization of strings and branes coupled to BF theoryPreprint
Baez, J. C., & Pérez, A. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0605087
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The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677 · see citing works
Extended matter coupled to BF theory
Fairbairn, W. J., & Perez, A. (2008) · Physical Review D · doi:10.1103/physrevd.78.024013 · Cited by 25 · see citing works
- Authors
- Freidel, L., Kowalski-Glikman, J., & Starodubtsev, A.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2006-10-02
- Volume
- 74
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2121603774
- Cited by
- 36
- References
- 17
- Citations by year
- 2026: 1 · 2025: 1 · 2023: 1 · 2021: 2 · 2020: 1 · 2019: 2 · 2017: 1 · 2016: 2 · 2015: 1 · 2014: 3 · 2013: 2 · 2012: 2
- FWCI
- 1.53
- 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)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Wilson lines, relativistic particles, particle spin, particle masses, gauge degrees of freedom, gauge-invariant observables
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