A Summary of the Asymptotic Analysis for the EPRL Amplitude
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We review the basic steps in building the asymptotic analysis of the Euclidean sector of new spin foam models using coherent states, for Immirzi parameter less than one. We try to focus on conceptual issues and by so doing omit peripheral proofs and the original discussion on spin structures.
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The Riemannian EPRL vertex asymptotics is the unbalanced square of the SU(2) asymptotics, and the resulting asymptotic formula is also valid for γ > 1.
“implies the asymptotic formula for the vertex amplitude to be given by the unbalanced square of the above formula [62], namely One can write the previous expression as 217”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [62]
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Research works printed but not linked: 9
- [2][2] A. Perez, 'Spin foam models for quantum gravity,' Classical and Quantum Gravity , vol. 20, p. R43, 2003. -
- [3][3] G. Ponzano and T. Regge, 'Semiclassical limit of racah coefficients,' in Spectroscopy and group theoretical methods in physics (F. Block, ed.), pp. 1-58, North Holland, 1968. -
- [4][4] J. W. Barrett and L. Crane, 'Relativistic spin networks and quantum gravity,' Journal of Mathematical Physics , vol. 39, p. 3296, 1998. -
- [5][5] J. W. Barrett and R. M. Williams, 'The asymptotics of an amplitude for the 4-simplex,' Advances in Theoretical and Mathematical Physics , vol. 3, p. 209, 1999. -
- [6][6] E. Alesci, 'Tensorial Structure of the LQG graviton propagator,' Int. J. Mod. Phys. , vol. A23, pp. 1209-1213, 2008, 0802.1201. -
- [7][7] J. Engle, E. Livine, R. Pereira, and C. Rovelli, 'LQG vertex with finite Immirzi parameter,' Nucl. Phys. , vol. B799, pp. 136-149, 2008, 0711.0146. -
- [8][8] E. R. Livine and S. Speziale, 'A new spinfoam vertex for quantum gravity,' Physical Review D , vol. 76, p. 084028, 2007. -
- [9][9] V. Guillemin and S. Sternberg, 'Geometric quantization and multiplicities of group representations.,' Invent. Math. , vol. 67 no.3, pp. 515-538, 1982. -
- [10][10] L. Hormander, The analysis of linear partial differential operators I . Springer-Verlag, 1983.
Cited by
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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
- Authors
- Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Gomes, H., Hellmann, F., Kowalski-Glikman, J., Durka, R., & Szczachor, M.
- Affiliations
- University of Nottingham (GB)
- Venue
- AIP Conference Proceedings
- Publisher
- AIP
- Published
- 2009
- Pages
- 36-43
- ISSN
- 0094-243X (ISSN-L)
- OpenAlex
- W2051222861
- Cited by
- 3
- References
- 0
- Citations by year
- 2021: 1 · 2013: 1
- FWCI
- 0.33
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- AIP conference proceedings (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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- EPRL model, spin foam models, asymptotic analysis, coherent states, Immirzi parameter, quantum gravity, spin structure
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