REVIEW 4 cited by
MacDowell-Mansouri gravity and Cartan geometry
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.
Forward citations
Cited by 4 Pith papers
-
Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
-
On quantum $G$-structures
A quantum G-structure, defined as a reduction of a quantum frame resolution, itself forms a quantum frame resolution under a covariant first-order differential calculus.
-
Particles, Forces and the Early Universe
The paper asserts a unified scenario of preon supersymmetry, no-boundary cosmology, and Chern-Simons gravity without providing new derivations or quantitative predictions.
-
Teleparallel gravity from the principal bundle viewpoint
TEGR is argued to admit a gauge theory formulation on principal bundles with Poincaré or Lorentz structure groups, where the gauge group is the diffeomorphism group if the teleparallel connection is not treated as an ...
Discussion (0). Sign in to comment.