Krein spaces in de Sitter quantum theories

Jean Pierre Gazeau*, Petr Siegl, Ahmed Youssef

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number011
JournalSymmetry, Integrability and Geometry: Methods and Applications
Publication statusPublished - 2010
Externally publishedYes


  • De Sitter group
  • Gupta-Bleuler
  • Krein spaces
  • Undecomposable representations

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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