Lifting SU(2) spin networks to projected spin networks
Open accessAbstract
Projected spin network states are the canonical basis of quantum states of geometry for the recent EPRL-FK spinfoam models for quantum gravity introduced by Engle-Pereira-Rovelli-Livine and Freidel-Krasnov. They are functionals of both the Lorentz connection and the time-normal field. We analyze in detail the map from these projected spin networks to the standard SU(2) spin networks of loop quantum gravity. We show that this map is not one to one and that the corresponding ambiguity is parameterized by the Immirzi parameter. We conclude with a comparison of the scalar products between projected spin networks and SU(2) spin network states.
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Special subclasses of projected spin networks appear naturally as boundary states of the new spin foams.
“The fact that these special subclasses of projected spin networks appear naturally as boundary states of the new spin foams is shown in [158].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [158]
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- Authors
- Dupuis, M., & Livine, E. R.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2010-09-30
- Volume
- 82
- Issue
- 6
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2111008219
- Cited by
- 71
- References
- 32
- Citations by year
- 2025: 3 · 2024: 3 · 2023: 1 · 2022: 2 · 2021: 5 · 2020: 2 · 2019: 4 · 2018: 3 · 2017: 4 · 2016: 6 · 2015: 3 · 2014: 6 · 2013: 7 · 2012: 13
- FWCI
- 6.58
- 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)
- arXiv (Cornell University)
- 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
- loop quantum gravity, Immirzi parameter, Lorentz connection, inner product
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