ON REAL MASSLESS SCALAR FIELD IN 2-DIMENSIONAL DESITTER SPACE-TIME

Quantum field theory of real massless scalar field in two-dimensional de Sitter space-time is considered. The scalar product in the subspace of pure Coulomb states is decomposed into irreducible unitary representations of the three-dimensional proper ortochronous Lorentz group. It is shown that the Coulomb field contains representations from the main series if the ''fine structure constant'' (defined in the text) alpha > 1. If 0 < alpha < 1, there is additionally a representation from the supplementary series. The eigenvalue of the Casimir operator for this representation is 1/4alpha(2-alpha).