The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
Quantization of point particles in (2 + 1)-dimensional gravity and spacetime discreteness
Open accessAbstract
By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three integers. Various representations are possible, the details depending on the topology chosen for energy-momentum space. We find that an $S_2\times S_1$ topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An $S_3$ topology also gives a lattice, but does not allow first quantized particles.
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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
General relativity without coordinates
Regge, T. (1961) · Il Nuovo Cimento · doi:10.1007/bf02733251 · Cited by 1,477
Three-dimensional Einstein gravity: Dynamics of flat space
Deser, S., Jackiw, R., & 't Hooft, G. (1984) · Annals of Physics · doi:10.1016/0003-4916(84)90085-x · Cited by 1,222
Recent Developments in Gravitation
(1979) · Springer eBooks · doi:10.1007/978-1-4613-2955-8 · Cited by 284
Classical and quantum scattering on a cone
Deser, S., & Jackiw, R. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01466729 · Cited by 282
Einstein's theory in a three-dimensional space-time
Giddings, S., Abbott, J., & Kuchař, K. (1984) · General Relativity and Gravitation · doi:10.1007/bf00762914 · Cited by 256
Non-perturbative 2 particle scattering amplitudes in 2+1 dimensional quantum gravity
't Hooft, G. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01218392 · Cited by 219
General relativity in a (2 + 1)-dimensional space-time
Gott, J. R., & Alpert, M. (1984) · General Relativity and Gravitation · doi:10.1007/bf00762539 · Cited by 216
Four-dimensional simplicial quantum gravity
Ambjørn, J., & Jurkiewicz, J. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90709-d · Cited by 205
Exact quantum scattering in 2 + 1 dimensional gravity
Carlip, S. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90183-1 · Cited by 153
Cited by
Tests of quantum gravity from observations of γ-ray bursts
Amelino-Camelia, G., Ellis, J., Mavromatos, N. E., Nanopoulos, D. V., & Sarkar, S. (1998) · Nature · doi:10.1038/31647 · Cited by 1,430
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
Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
Amelino-Camelia, G., Ellis, J. R., Nanopoulos, D. V., Nanopoulos, D. V., & Sarkar, S. (1997) · CERN Document Server (European Organization for Nuclear Research) · doi:10.48550/arxiv.astro-ph/9712103 · Cited by 648
The Cellular Automaton Interpretation of Quantum Mechanics
't Hooft, G. (2016) · Fundamental Theories of Physics · doi:10.1007/978-3-319-41285-6 · Cited by 355
Quantum mechanics of a point particle in -dimensional gravity
Matschull, H.-J., & Welling, M. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/10/008 · Cited by 176
Metadata
- Authors
- Hooft, G. '.
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1996-05-01
- Volume
- 13
- Issue
- 5
- Pages
- 1023-1039
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2006974785
- Cited by
- 332
- References
- 38
- FWCI
- 10.53
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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