gravity as a BF theory in nLab
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Physics
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theory (physics), model (physics)
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Axiomatizations
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Tools
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Structural phenomena
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Types of quantum field thories
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Contents
Idea
The Palatini- or first order formulation of the Einstein-Hilbert action for gravity is
where
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is the curvature of an -connection
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is the vielbein.
This is reminiscent of the form of the action functional in BF theory
Various proposals for extensions of this action functional have been made that feature as an independent field as indicated but then include some dynamical constraint which ensures that on-shell one has .
This is also related to the Plebanski formulation of gravity.
References
The blog entry
- Jacques Distler, BF (blog)
recalls the construction of
- Laurent Freidel, Artem Starodubtsev, Quantum gravity in terms of topological observables (arXiv)
and provides some noteworthy comments.
Approaches using the spin group instead of the rotation group include
- Jerzy Lewandowski, Andrzej Okolow, 2-Form Gravity of the Lorentzian signature (arXiv)
and
- Han-Ying Guo, Yi Ling, Roh-Suan Tung, Yuan-Zhong Zhang, Chern-Simons Term for BF Theory and Gravity as a Generalized Topological Field Theory in Four Dimensions (arXiv)
For that spinorial approach see also
- Roh Suan Tung, Ted Jacobson, Spinor One-forms as Gravitational Potentials (arXiv)
See also
- R. Capovilla, M. Montesinos, V. A. Prieto, E. Rojas, BF gravity and the Immirzi parameter (arXiv)
Related is also the construction in
- Michael P. Reisenberger, Classical Euclidean general relativity from “left-handed area = right-handed area” (arXiv)
A blog discussion about this and possible interpretations in higher category theory is at
- Urs Schreiber, 2-Palatini (blog)
Last revised on September 22, 2010 at 16:29:00. See the history of this page for a list of all contributions to it.