  In this letter we show that the ``preferred'' Klein-Gordon Quantum Field
Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a
Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime
satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a
(d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral
condition can be obtained as superposition of d-dimensional de Sitter
Klein-Gordon fields in the preferred vacuum. These results establish a
correspondence between QFT's living on manifolds having different dimensions.
The method exposed here can be applied to study other situations and notably
QFT on Anti de Sitter spacetime.

High Energy Physics - Theory;General Relativity and Quantum Cosmology