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This article is cited in 13 scientific papers (total in 13 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.
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.
Linking options:
https://www.mathnet.ru/eng/sigma468 https://www.mathnet.ru/eng/sigma/v6/p11
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