Quantum Field Theory in de Sitter space : A survey of recent approaches

We present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. For the "massive'' cases which are associated to principal series representations of the de Sitter group SO\_0(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.