Krein Spaces in de Sitter Quantum Theories

Abstract

Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group $S{O}_0(1,4)$ or $Sp(2,2)$ as an appealing substitute to the flat space-time Poincare 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.

References in corpus (9)

• The Physics of Cosmic Acceleration
• Two-point Functions and Quantum Fields in de Sitter Universe
• Modular localization and Wigner particles
• Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
• Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space
• Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time
• De Sitter Waves and the Zero Curvature Limit
• Resource Letter: Dark Energy and the Accelerating Universe
• A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"

Cited by in corpus (5)

• Shift Symmetries in (Anti) de Sitter Space
• Quantum Field Theory in de Sitter Universe: Ambient Space Formalism
• Particle Creation in Global de Sitter Space: Bulk Space Consideration
• Conceptual and technical challenges of quantum gravity
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation