An Introduction to Quantum Field Theory in de Sitter space-time

International audienceThe aim of these lectures is to present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. We will particularly emphasize the symmetry principles ruling the construction of these quantum fields. For the "massive" cases which are associated to the principal series representations of the de Sitter group SO(1,4), the construction is based on analyticity requirements on the Wightman two-point function. For the "massless" cases ( e.g., minimally coupled or conformal), associated to the discrete series, the quantization schemes are of the Gupta-Bleuler-Krein type