Some properties of the two-point functions in a dilatationally covariant field theory

The object of our concern are some properties of the two-point functions in a model of dilatationally covariant field theory. We examine the one- and two-dimensional irreducible representations of the dilatation group. For the one-dimensional case we obtain either a massless free field theory or a theory of an interacting field which does not contribute on the mass shell μ=p²=0 and is characterized by a spectral function μ^r₊?1. In the two-dimensional case both fields differ from the free field, their spectral functions ρ_ij(μ) do not vanish identically and are products of two factors, a polynomial of order up to two in ln μ and μ^r₊?-1. The differences between the case of internal symmetry and the case of dilatations are emphasized. The formula for the form factor in the Araki-Haag limit is given.