Sum rules for few-particle scattering in two dimensions

The authors report on some new results in the study of sum rules in many-particle scattering. In particular, they consider two-dimensional scattering, which has received some new attention recently, especially in connection with the discussion of monolayers of quantum gases. The method of derivation is based upon a detailed study of the analyticity properties of the Green's functions involved, especially their high-energy expansions, together with a contour integration in the complex-energy plane, around the spectrum of the many-particle Hamiltonian. (Auth.)