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 represe
ntations of the three-dimensional proper ortochronous Lorentz group. I
t is shown that the Coulomb field contains representations from the ma
in series if the ''fine structure constant'' (defined in the text) alp
ha > 1. If 0 < alpha < 1, there is additionally a representation from
the supplementary series. The eigenvalue of the Casimir operator for t
his representation is 1/4alpha(2-alpha).