A pure spin-connection formulation of gravity
Open accessAbstract
A new action principle, in which the only gravitational variables are an SL(2,C) connection and a scalar density, is derived for general relativity (GR) coupled to matter and for supergravity. In this form, GR appears as a non-metric, generally covariant gauge theory, the metric being reconstructed from the other fields in a solution. A similar non-metric action with a real SO(3,1) connection is also derived, however it involves an independent fourth rank tensor field representing the curvature.
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Flat geometries are not contained in the sector of gravity described by the Capovilla-Dell-Jacobson formulation.
“In particular, flat geometries are not contained in this sector.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
In the Capovilla-Dell-Jacobson formulation of general relativity, the integration over the e variables is partially performed at the continuum level.
“In the Capovilla-Dell-Jacobson [110, 109] formulation of general relativity this ‘integration’ is partially performed at the continuum level.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
The Capovilla-Dell-Jacobson formulation corresponds to a sector of gravity in which the Weyl tensor satisfies certain algebraic requirements.
“One serious problem of this formulation is that it corresponds to a sector of gravity where the Weyl tensor satisfies certain algebraic requirements.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [110]
In the generic case where E_ab are linearly independent, conditions (5) and (6) admit exactly three sorts of solutions in addition to E_ab=e_a∧e_b.
“In the generic case, when the E ab (a < b) are linearly independent, it can be shown [20,22] that conditions (5) and (6) admit exactly three sorts of solutions in addition to those of the form”
From Spin foam models (1998) · cites this paper as [22]
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- Authors
- Capovilla, R., Dell, J., & Jacobson, T.
- Affiliations
- University of Maryland, College Park (US)
- ORCID
- Capovilla, R
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1991-01-01
- Volume
- 8
- Issue
- 1
- Pages
- 59-73
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1972877551
- Cited by
- 162
- References
- 10
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2023: 3 · 2021: 4 · 2020: 2 · 2019: 3 · 2018: 1 · 2017: 3 · 2016: 5 · 2015: 10 · 2014: 3 · 2013: 5 · 2012: 3
- FWCI
- 21.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- general relativity, supergravity, Hamilton's principle, scalar density, metric reconstruction, matter coupling
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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