Twistor networks and covariant twisted geometries
Open accessAbstract
We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of Engle, Pereira, Rovelli, Livine and Freidel, Krasnov spin foam models. Finally, we give an expression for the Haar measure in terms of spinors.
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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 [256]
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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
Generalized quantum gravity condensates for homogeneous geometries and cosmology
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- Authors
- Livine, E. R., Speziale, S., & Tambornino, J.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- ORCID
- Livine, Etera R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2012-03-02
- Volume
- 85
- Issue
- 6
- Pages
- 064002
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2030185009
- Cited by
- 41
- References
- 28
- Citations by year
- 2025: 2 · 2021: 3 · 2019: 2 · 2018: 1 · 2017: 5 · 2016: 2 · 2015: 4 · 2014: 7 · 2013: 8 · 2012: 7
- FWCI
- 6.30
- 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)
- 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
- twistors, symplectic reduction, Lorentz group, spinors, Haar measure, phase space
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