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http://arxiv.org/abs/gr-qc/0611154

Derek K. Wise

34 pages, 5 figures

"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 recent reformulation in terms of BF theory, in the context of Cartan geometry."

things to notice:

care was taken to be intuitive and explain conceptually so as to generate more understanding----a certain bundle was described in terms of a hamster

the paper topics are what JB had that thread about earlier. Cartan geometry, rolling without slipping. JB had that thread about the forthcoming Baratin Freidel paper.

Derek Wise is doing his PhD thesis at UCR with Baez as advisor, but I think he also spent some time at Perimeter this year.

it is really nicely written.

the acknowledgments read like a list of people working on a certain approach that we've gotten some news about:

"..Acknowledgments

I thank John Baez, Aristide Baratin, Jim Dolan, Laurent Freidel, Bill Goldman, Jeff Morton,

Artem Starodubtsev, Danny Stevenson, and Josh Willis for helpful discussions..."

**MacDowell-Mansouri gravity and Cartan geometry**Derek K. Wise

34 pages, 5 figures

"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 recent reformulation in terms of BF theory, in the context of Cartan geometry."

things to notice:

care was taken to be intuitive and explain conceptually so as to generate more understanding----a certain bundle was described in terms of a hamster

the paper topics are what JB had that thread about earlier. Cartan geometry, rolling without slipping. JB had that thread about the forthcoming Baratin Freidel paper.

Derek Wise is doing his PhD thesis at UCR with Baez as advisor, but I think he also spent some time at Perimeter this year.

it is really nicely written.

the acknowledgments read like a list of people working on a certain approach that we've gotten some news about:

"..Acknowledgments

I thank John Baez, Aristide Baratin, Jim Dolan, Laurent Freidel, Bill Goldman, Jeff Morton,

Artem Starodubtsev, Danny Stevenson, and Josh Willis for helpful discussions..."

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