Twistorial phase space for complex Ashtekar variables
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We generalize the SU (2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group . We show that the phase space for complex-valued Ashtekar variables on a spin-network graph can be decomposed in terms of twistorial variables. To every link there are two twistors—one to each boundary point—attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.
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The constraint solution p = γj and k = j also follows naturally from a spinor formulation of the simplicity constraints.
“More recently, it has been shown that the constraint solution p = γj and k = j also follows naturally from a spinor formulation of the simplicity constraints [369, 156, 256].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [369]
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Flagged first, then by citations
Research works printed but not linked: 13
- Livine E R and Tambornino J 2011 Spinor representation for loop quantum gravity arXiv:1105.3385 · arXiv
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Sorted by citations
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
Generalized quantum gravity condensates for homogeneous geometries and cosmology
Oriti, D., Pranzetti, D., Ryan, J. P., & Sindoni, L. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/23/235016 · Cited by 48 · see citing works
Twistor networks and covariant twisted geometries
Livine, E. R., Speziale, S., & Tambornino, J. (2012) · Physical Review D · doi:10.1103/physrevd.85.064002 · Cited by 41 · see citing works
- Authors
- Wieland, W. M.
- Affiliations
- Centre de Physique Théorique (FR)
- Corresponding author
- Wieland, Wolfgang M
- ORCID
- Wieland, Wolfgang M
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2012-02-02
- Volume
- 29
- Issue
- 4
- Pages
- 045007
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2043086602
- Cited by
- 33
- References
- 15
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 3 · 2023: 2 · 2021: 1 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 5 · 2016: 1 · 2015: 2 · 2014: 4 · 2013: 2 · 2012: 3
- FWCI
- 2.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (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
- twisted geometry, spin networks, simplicity constraints, loop quantum gravity
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