New algebraic approach to scattering problems

Quantum scattering systems described by Hamiltonians which are constructed from the Casimir operators of certain noncompact groups G are considered. We obtain the following result: If U-chi and C(<(chi)over bar>) are the Weyl-equivalent representations of the symmetry group G of the dynamical system, the corresponding S matrices are constrained to satisfy SUchi(g) = U(<(chi)over bar>)(g)S, for all g is an element of G. This relation enables one to derive S. As applications, the S matrices corresponding to the dynamical groups SO0(p,q) are derived.