We present a quantization scheme of an arbitrary measure space based on overcomplete families of states and generalizing the Klauder and the Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods like geometric quantization are uneasy to implement. The procedure is… (More)
We present in this paper a fully covariant quantization of the minimally-coupled mass-less field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-Gärding axiomatic for mass-less… (More)
We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This… (More)
We show that the coherent state quantization of massive particles in 1+1 de Sitter space exhibits an ordering property: There exist some classical observables A and A * such that O A * p O A q = O A * p A q p, q ∈ Z, where O A is the quantum observable corresponding to the classical observable A.
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 two-points… (More)