Self-dual 2-forms and gravity
Abstract
A Palatini-type formulation of gravity coupled to matter and supergravity is given, in which the gravitational variables are a trio of self-dual 2-forms and an SL(2,C) connection. The action is polynomial in all the fields. This framework is shown to be the natural covariantization of Ashtekar's canonical formalism (1988), and is used to find the general vacuum solution of the four initial value constraints associated with spacetime diffeomorphisms in that formalism.
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The Plebanski Lagrangian for general relativity has the form of BF theory with gauge group SL(2,C), with an added term which is a constraint.
“In fact, the Plebanski Lagrangian [8,9] for general relativity has the form of BF theory [10] with gauge group SL(2 , C ), with an added term which is a constraint.”
From Relativistic spin networks and quantum gravity (1998) · cites this paper as [9]
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References 27 · Cited by 286
- Authors
- Capovilla, R., Dell, J., Jacobson, T., & Mason, L.
- Affiliations
- University of Maryland, College Park (US)
- ORCID
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1991-01-01
- Volume
- 8
- Issue
- 1
- Pages
- 41-57
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1987344724
- Cited by
- 286
- References
- 27
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 6 · 2023: 15 · 2022: 3 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 5 · 2017: 5 · 2016: 8 · 2015: 6 · 2014: 9 · 2013: 11 · 2012: 12
- FWCI
- 30.67
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- 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
- Keywords
- Palatini formulation, supergravity, covariantization, diffeomorphism invariance, vacuum solutions
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