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 SO_0(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 represen...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-01-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.011 |
| _version_ | 1818139773052649472 |
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| author | Ahmed Youssef Petr Siegl Jean-Pierre Gazeau |
| author_facet | Ahmed Youssef Petr Siegl Jean-Pierre Gazeau |
| author_sort | Ahmed Youssef |
| collection | DOAJ |
| description | Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO_0(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. |
| first_indexed | 2024-12-11T10:33:25Z |
| format | Article |
| id | doaj.art-aecfb728f1ff4192a4135795cd6ba2b8 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-11T10:33:25Z |
| publishDate | 2010-01-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-aecfb728f1ff4192a4135795cd6ba2b82022-12-22T01:10:50ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-01-016011Krein Spaces in de Sitter Quantum TheoriesAhmed YoussefPetr SieglJean-Pierre GazeauExperimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO_0(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.http://dx.doi.org/10.3842/SIGMA.2010.011de Sitter groupundecomposable representationsKrein spacesGupta-Bleuler tripletcohomology of representations |
| spellingShingle | Ahmed Youssef Petr Siegl Jean-Pierre Gazeau Krein Spaces in de Sitter Quantum Theories Symmetry, Integrability and Geometry: Methods and Applications de Sitter group undecomposable representations Krein spaces Gupta-Bleuler triplet cohomology of representations |
| title | 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_short | Krein Spaces in de Sitter Quantum Theories |
| title_sort | krein spaces in de sitter quantum theories |
| topic | de Sitter group undecomposable representations Krein spaces Gupta-Bleuler triplet cohomology of representations |
| url | http://dx.doi.org/10.3842/SIGMA.2010.011 |
| work_keys_str_mv | AT ahmedyoussef kreinspacesindesitterquantumtheories AT petrsiegl kreinspacesindesitterquantumtheories AT jeanpierregazeau kreinspacesindesitterquantumtheories |