Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
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 w...
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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149140 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149140 |
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dspace |
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irk-123456789-1491402019-02-20T01:25:33Z Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions Wise, D.K. 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'. 2009 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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'. |
| format |
Article |
| author |
Wise, D.K. |
| spellingShingle |
Wise, D.K. Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Wise, D.K. |
| author_sort |
Wise, D.K. |
| title |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions |
| title_short |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions |
| title_full |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions |
| title_fullStr |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions |
| title_full_unstemmed |
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions |
| title_sort |
symmetric space cartan connections and gravity in three and four dimensions |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149140 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT wisedk symmetricspacecartanconnectionsandgravityinthreeandfourdimensions |
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2023-05-20T17:32:24Z |
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2023-05-20T17:32:24Z |
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