Krein Spaces in de Sitter Quantum Theories
Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1,4) or Sp(2,2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible represent...
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| Дата: | 2010 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146149 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Krein Spaces in de Sitter Quantum Theories / J.P. Gazeau, P. Siegl, A. Youssef // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146149 |
|---|---|
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dspace |
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irk-123456789-1461492019-02-08T01:24:05Z Krein Spaces in de Sitter Quantum Theories Gazeau, J.P. Siegl, P. Youssef, A. Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1,4) or Sp(2,2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecomposable representation cohomology which deserves to be thoroughly studied in view of quantization of the corresponding carrier fields. The purpose of this note is to present the mathematical material needed to examine the problem and to indicate possible extensions of an exemplary case, namely the so-called de Sitterian massless minimally coupled field, i.e. a scalar field in de Sitter space-time which does not couple to the Ricci curvature. 2010 Article Krein Spaces in de Sitter Quantum Theories / J.P. Gazeau, P. Siegl, A. Youssef // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T20; 81R05; 81R20; 22E70; 20C35 http://dspace.nbuv.gov.ua/handle/123456789/146149 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 |
Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1,4) or Sp(2,2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecomposable representation cohomology which deserves to be thoroughly studied in view of quantization of the corresponding carrier fields. The purpose of this note is to present the mathematical material needed to examine the problem and to indicate possible extensions of an exemplary case, namely the so-called de Sitterian massless minimally coupled field, i.e. a scalar field in de Sitter space-time which does not couple to the Ricci curvature. |
| format |
Article |
| author |
Gazeau, J.P. Siegl, P. Youssef, A. |
| spellingShingle |
Gazeau, J.P. Siegl, P. Youssef, A. Krein Spaces in de Sitter Quantum Theories Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gazeau, J.P. Siegl, P. Youssef, A. |
| author_sort |
Gazeau, J.P. |
| title |
Krein Spaces in de Sitter Quantum Theories |
| title_short |
Krein Spaces in de Sitter Quantum Theories |
| title_full |
Krein Spaces in de Sitter Quantum Theories |
| title_fullStr |
Krein Spaces in de Sitter Quantum Theories |
| title_full_unstemmed |
Krein Spaces in de Sitter Quantum Theories |
| title_sort |
krein spaces in de sitter quantum theories |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146149 |
| citation_txt |
Krein Spaces in de Sitter Quantum Theories / J.P. Gazeau, P. Siegl, A. Youssef // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 31 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT gazeaujp kreinspacesindesitterquantumtheories AT sieglp kreinspacesindesitterquantumtheories AT youssefa kreinspacesindesitterquantumtheories |
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2023-05-20T17:23:57Z |
| last_indexed |
2023-05-20T17:23:57Z |
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1796153208796610560 |