v2 is is the definitive (improved compare to v1) versionInternational audienceIn this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO0(2,4) group and consequently under the de Sitter group. We obtain a new de Sitter-invariant two-point function which is very simple. Our method relies on the one hand on a geometrical point of view which uses the realization of Minkowski, de Sitter and anti-de Sitter spaces as intersections of the null cone in R6 and a moving plane, and on the other hand on a canonical quantization scheme of the Gupta-Bleuler type

In this paper we write down the equation for a scalar conformally coupled field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski spacetime in d dimensions. The curvature dependence appears in a very simple way through a conformal factor. As a consequence the process of curvature free limit, including wave functions limit and twopoints functions, turns to be a straightforward issue. We determine a set of modes, that we call de Sitter plane waves, which become ordinary plane waves when the curvature vanishes.