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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Sprache: | English |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146149 |
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| Zitieren: | 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. |
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Gazeau, J.P. Siegl, P. Youssef, A. 2019-02-07T19:05:51Z 2019-02-07T19:05:51Z 2010 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 https://nasplib.isofts.kiev.ua/handle/123456789/146149 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. This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The full collection is available at http://www.emis.de/journals/SIGMA/Prague2009.html. Throughout this text, for convenience, we will mostly work in units c = 1 = ~, for which R = H−1, while restoring physical units when is necessary. P. Siegl appreciates the support of CTU grant No.CTU0910114 and MSMT project No.LC06002 en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Krein Spaces in de Sitter Quantum Theories Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Krein Spaces in de Sitter Quantum Theories |
| spellingShingle |
Krein Spaces in de Sitter Quantum Theories Gazeau, J.P. Siegl, P. Youssef, A. |
| 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 |
| author |
Gazeau, J.P. Siegl, P. Youssef, A. |
| author_facet |
Gazeau, J.P. Siegl, P. Youssef, A. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
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AT gazeaujp kreinspacesindesitterquantumtheories AT sieglp kreinspacesindesitterquantumtheories AT youssefa kreinspacesindesitterquantumtheories |
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2025-12-01T05:17:09Z |
| last_indexed |
2025-12-01T05:17:09Z |
| _version_ |
1850859363337502720 |