TwoPoint Functions and Quantum Fields in de Sitter Universe
Abstract
We present a theory of general twopoint functions and of generalized free fields in ddimensional de Sitter spacetime which closely parallels the corresponding Minkowskian theory. The usual spectral condition is now replaced by a certain geodesic spectral condition, equivalent to a precise thermal characterization of the corresponding “vacuum” states. Our method is based on the geometry of the complex de Sitter spacetime and on the introduction of a class of holomorphic functions on this manifold, called perikernels, which reproduce mutatis mutandis the structural properties of the twopoint correlation functions of the Minkowskian quantum field theory. The theory contains as basic elementary case the linear massive field models in their “preferred” representation. The latter are described by the introduction of de Sitter plane waves in their tube domains which lead to a new integral representation of the twopoint functions and to a FourierLaplace type transformation on the hyperboloid. The Hilbert space structure of these theories is then analysed by using this transformation. In particular we show the ReehSchlieder property. For general twopoint functions, a substitute to the Wick rotation is defined both in complex spacetime and in the complex mass variable, and substantial results concerning the derivation of KällenLehmann type representation are obtained.
 Publication:

Reviews in Mathematical Physics
 Pub Date:
 1996
 DOI:
 10.1142/S0129055X96000123
 arXiv:
 arXiv:grqc/9511019
 Bibcode:
 1996RvMaP...8..327B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 51 p, uuencoded, LaTex, epsf, 2 figures included