Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
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| Creator |
Wise, D.K.
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| Description |
Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action. In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model. I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1) and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'.
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| Date |
2019-02-19T17:38:16Z
2019-02-19T17:38:16Z 2009 |
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| Type |
Article
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| Identifier |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions / D.K. Wise // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 40 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 22E70; 51P05; 53C80; 83C80; 83C99 http://dspace.nbuv.gov.ua/handle/123456789/149140 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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