New vertices and canonical quantization
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We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to loop quantum gravity. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstrained BF theory.
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In the Riemannian Gupta-Bleuler approach with γ > 1, restricting Spin(4) representations to the minimum-weight component j = j+ − j− satisfies the relevant condition.
“Case γ > 1: In this case [13] one restricts the Spin(4) representations to 131 which amounts to choosing the minimum weight component j = j+ − j− in the expansion (182). This choice of is the solution to condition (188).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [13]
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- Authors
- Alexandrov, S.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- Corresponding author
- Alexandrov, Sergei
- ORCID
- Alexandrov, Sergei
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2010-07-19
- Volume
- 82
- Issue
- 2
- Pages
- 024024
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2106127942
- Cited by
- 48
- References
- 34
- Citations by year
- 2023: 1 · 2021: 3 · 2020: 1 · 2019: 1 · 2018: 2 · 2016: 2 · 2015: 3 · 2014: 3 · 2013: 5 · 2012: 11
- FWCI
- 7.26
- 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)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Agence Nationale de la Recherche (ANR-09-BLAN-0041)
- 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
- spin foam models, loop quantum gravity, canonical quantization, BF theory, symplectic structure, quantum gravity
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