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SIGMA, 2010, Volume 6, 011, 23 pages (Mi sigma468)  

This article is cited in 8 scientific papers (total in 8 papers)

Krein Spaces in de Sitter Quantum Theories

Jean-Pierre Gazeaua, Petr Sieglba, Ahmed Youssefa

a Astroparticules et Cosmologie (APC, UMR 7164), Université Paris-Diderot, Boite 7020, 75205 Paris Cedex 13, France
b Nuclear Physics Institute of Academy of Sciences of the Czech Republic, 250 68 Rez, Czech Republic

Abstract: 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.

Keywords: de Sitter group; undecomposable representations; Krein spaces; Gupta–Bleuler triplet, cohomology of representations


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ArXiv: 1001.4810
MSC: 81T20; 81R05; 81R20; 22E70; 20C35
Received: October 19, 2009; in final form January 15, 2010; Published online January 27, 2010

Citation: Jean-Pierre Gazeau, Petr Siegl, Ahmed Youssef, “Krein Spaces in de Sitter Quantum Theories”, SIGMA, 6 (2010), 011, 23 pp.

Citation in format AMSBIB
\by Jean-Pierre Gazeau, Petr Siegl, Ahmed Youssef
\paper Krein Spaces in de Sitter Quantum Theories
\jour SIGMA
\yr 2010
\vol 6
\papernumber 011
\totalpages 23

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    This publication is cited in the following articles:
    1. Pérez-Nadal G., Roura A., Verdaguer E., “Stress tensor fluctuations in de Sitter spacetime”, J. Cosmol. Astropart. Phys., 2010, no. 5, 036  crossref  mathscinet  isi  scopus
    2. Gazeau J.-P., Novello M., “The nature of $\Lambda$ and the mass of the graviton: a critical view”, Internat. J. Modern Phys. A, 26:22 (2011), 3697–3720  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Znojil M., “$N$-site-lattice analogues of $V(x)=ix^3$”, Ann. Physics, 327:3 (2012), 893–913  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Fathi M., Tanhayi-Ahari M., Tanhayi M.R., Tavakoli F., “Radiation Effects on Geodesics in de Sitter Space: a Classical Approach”, Int. J. Theor. Phys., 51:6 (2012), 1938–1945  crossref  mathscinet  zmath  isi  scopus
    5. Mirabi S., “Massive Fermion Particle Production in de Sitter Universe: Ambient Space Approach”, Mod. Phys. Lett. A, 29:10 (2014), 1400001  crossref  isi  scopus
    6. Tanhayi M.R., “Particle Creation in Global de Sitter Space: Bulk Space Consideration”, Int. J. Mod. Phys. D, 24:7 (2015), 1550052  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Tanhayi M.R., Mohsenzadeh M., Yusofi E., “Plane waves in de Sitter space: Spin- $\frac{1}{2}$ field”, Eur. Phys. J. Plus, 131:6 (2016), 198  crossref  isi  scopus
    8. Bonifacio J., Hinterbichler K., Joyce A., Rosen R.A., “Shift Symmetries in (Anti) de Sitter Space”, J. High Energy Phys., 2019, no. 2, 178  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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