The EPRL intertwiners and corrected partition function
Open accessAbstract
Do the SU (2) intertwiners parametrize the space of the Engle, Pereira, Rovelli, Livine (EPRL) solutions to the simplicity constraint? What is the complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective in the general n -valent vertex case for the Barbero–Immirzi parameter less than 1. We find, however, that the EPRL map is not isometric. In the consequence, a partition function can be defined either using the EPRL intertwiners Hilbert product or the SU (2) intertwiners Hilbert product. We use the EPRL one and derive a new, complete formula for the partition function. Next, we view it in terms of the SU (2) intertwiners. The result, however, goes beyond the SU (2) spin-foam models' framework and the original EPRL proposal.
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A consistent modification of the EPRL model can be obtained by replacing the non-projector object with a genuine projector.
“As proposed in [49, 235] one can obtain a consistent modification of the EPRL model by replacing (167) by a genuine projector , graphically 168”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [235]
The requirement of anomaly freedom under the discrete symmetry can be met by suitable definitions of the transition amplitudes.
“We have seen that this requirement (advocated in [90]) can be met by suitable definitions of the transition amplitudes [49, 235]”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [235]
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- Authors
- Kamiński, W., Kisielowski, M., & Lewandowski, J.
- Affiliations
- University of Warsaw (PL)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2010-07-08
- Volume
- 27
- Issue
- 16
- Pages
- 165020
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2051850811
- Cited by
- 43
- References
- 15
- Citations by year
- 2021: 2 · 2019: 3 · 2018: 2 · 2016: 3 · 2014: 8 · 2013: 8 · 2012: 6
- FWCI
- 5.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0456913)
- European Science Foundation
- Fundacja na rzecz Nauki Polskiej
- 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
- simplicity constraints, Barbero-Immirzi parameter, isometries, quantum gravity, spin foam models
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