Construction of local relativistic quantum fields on de Sitter space-times from random fields on spheres

The aim of this project is to investigate in which manner random fields on spheres are related to quantum fields on de Sitter spaces. De Sitter spaces are hyperboloids equipped with a causal structure, which is essentially determined by the maximal propagation speed of light. Thus de Sitter spaces provide a simple model of space-times in the sense of the theory of general relativity. The quantum fields should be constructed from the random fields by analytic continuation. First of all the axiomatic porperties of the quantum fields should be investigated. One expects a quantum field theory in indefinite metric, i.e. the quantum mechanical state space is not given uniquely. In the next step the scattering behaviour of the quantum fields is to be considered. Scattering theory describes the way how quantum fields in the past are mapped on those in the future. In this context a non-trivial scattering behaviour may be verified Moreover, the models under consideration show a rather weak singular behaviour, which could possibly allow also the study of perturbation by certain potentials.