- Access by Xinjiang University
Hamiltonian form of Carroll gravity
Phys. Rev. D 107, 024010 – Published 12 January, 2023
DOI: https://doi.org/10.1103/PhysRevD.107.024010
Abstract
We develop a Hamiltonian description of the “Carroll” (Levy Leblond-Sen Gupta) limit of gravity theory in the first-order formalism. Through a constraint analysis, the number of local degrees of freedom are shown to be two in this singular limit. The Hamiltonian constraint in this (“magnetic”) limit depends only on the densitized triad fields and their space derivatives. We also provide a scaling prescription within the Hilbert-Palatini theory to obtain the first-order analogue of the “electric” limit of canonical metric gravity. The simplicity of both these limiting Hamiltonian forms in these variables make them interesting candidates for quantization.
Physics Subject Headings (PhySH)
Article Text
References (28)
- J. M. Levy-Leblond, Ann. Inst. Henri Poincare, 3, 1 (1965).
- N. D. Sen Gupta, Nuovo Cimento 44, 512 (1966).
- H. Bacry and J. M. Levy-Leblond, J. Math. Phys. (N.Y.) 9, 1605 (1968).
- C. Teitelboim, Surface deformations, their square root and the signature of space-time, in Proceedings of the 7th International Group Theory Colloquium: The Integrative Conference on Group Theory and Mathematical Physics, Austin Group Theory, Report No. Print-78-1134 (Princeton, NJ, 1978), 362; Ann. Phys. (N.Y.) 79, 542 (1973).
- M. Henneaux, Bull. Soc. Math. Belg. 31, 47 (1979).
- V. A. Belinsky, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 19, 525 (1970); 31, 639 (1982).
- T. Damour, M. Henneaux, and H. Nicolai, Classical Quantum Gravity 20, R145 (2003).
- G. Dautcourt, Acta Phys. Pol. B 29, 1047 (1998).
- L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, Phys. Rev. D 100, 046010 (2019); L. Donnay and C. Marteau, Classical Quantum Gravity 36, 165002 (2019).
- G. Gibbons, K. Hashimoto, and P. Yi, J. High Energy Phys. 09 (2002) 061.
- C. Duval, G. W. Gibbons, P. A. Horvathy, and P.-M. Zhang, Classical Quantum Gravity 34, 175003 (2017).
- L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, J. High Energy Phys. 07 (2018) 165; A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, 12 (2016) 147.
- J. de Boer, J. Hartong, N. A. Obers, W. Sybesma, and S. Vandoren, Front. Phys. 10, 810405 (2022).
- E. Ekiz, O. Kasikci, M. Ozkan, C. B. Senisik, and U. Zorba, J. High Energy Phys. 10 (2022) 151.
- R. K. Kaul and S. Sengupta, Phys. Rev. D 93, 084026 (2016); 94, 104047 (2016).
- J. Hartong, J. High Energy Phys. 08 (2015) 069.
- E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel, and T. ter Veldhuis, J. High Energy Phys. 03 (2017) 165.
- A. Guerrieri and R. F. Sobreiro, Classical Quantum Gravity 38, 245003 (2021); J. Figueroa-O’Farrill, E. Have, S. Prohazka, and J. Salzer, J. High Energy Phys. 09 (2022) 243.
- D. Hansen, N. A. Obers, G. Oling, and B. T. Søgaard, SciPost Phys. 13, 055 (2022).
- M. Henneaux and P. Salgado-Rebolledo, J. High Energy Phys. 11 (2021) 180.
- M. Le Bellac and J.-M. Levy-Leblond, Nuovo Cimento B 14, 217 (1973).
- A. Ashtekar, A. Henderson, and D. Sloan, Classical Quantum Gravity 26, 052001 (2009); Phys. Rev. D 83, 084024 (2011).
- P. Peldan, Classical Quantum Gravity 11, 1087 (1994); N. Barros e Sa, Int. J. Mod. Phys. D 10, 261 (2001).
- G. Date, R. K. Kaul, and S. Sengupta, Phys. Rev. D 79, 044008 (2009); R. K. Kaul and S. Sengupta, 85, 024026 (2012).
- A. Raychaudhuri, Phys. Rev. 98, 1123 (1955).
- S. W. Hawking, Proc. R. Soc. A 294, 511 (1966).
- S. Sengupta, arXiv:2210.15980.
- A. Campoleoni, M. Henneaux, S. Pekar, A. Perez, and P. Salgado-Rebolledo, J. High Energy Phys. 09 (2022) 127.
