Holomorphic Lorentzian simplicity constraints
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We develop a Hamiltonian representation of the ${\mathfrak {sl}}(2,{\mathbb C})$sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including ${\mathfrak {gl}}(N,{\mathbb C})$gl(N,C) as a subalgebra. Then, we define the linear and quadratic simplicity constraints which reduce the spinor variables to (framed) 3d space-like polyhedra embedded in Minkowski spacetime. Finally, we introduce a new version of the simplicity constraints which (i) are holomorphic and (ii) Poisson-commute with each other, and show their equivalence to the linear and quadratic constraints.
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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 [156]
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References 26 · Cited by 64
Research works printed but not linked: 1
- [28]R. Penrose and W. Rindler, Spinors And Space-time. Vol. 2 , Cambridge, Uk: Univ. Pr. ( 1986) 501p.
- Authors
- Dupuis, M., Freidel, L., Livine, E. R., & Speziale, S.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Perimeter Institute (CA)
- Centre de Physique Théorique 4 , CNRS-Luminy Case 907, 13288 Marseille Cedex 09, France
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2012-03-01
- Volume
- 53
- Issue
- 3
- Pages
- 032502
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2079203628
- Cited by
- 64
- References
- 26
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2023: 1 · 2022: 1 · 2021: 4 · 2020: 4 · 2019: 4 · 2018: 1 · 2017: 5 · 2016: 4 · 2015: 6 · 2014: 10 · 2013: 15 · 2012: 4
- FWCI
- 8.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- simplicity constraints, twistors, global invariants, Minkowski space, Hamiltonian formulation
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