Exactly solvable models of scattering with SL(2, C) symmetry

Abstract

Using the theory of induced representations two exactly solvable models of non-relativistic scattering with SL(2, C) symmetry are presented. The first describes the scattering of a charged particle moving on the Poincare upper half space H under the influence of an SU(2) non-Abelian gauge potential with isospin s. The second deals with a one-dimensional coupled-channel scattering problem for a charged particle in a matrix-valued scalar potential containing Morse-like interaction terms. The coupled channel wavefunctions and the corresponding scattering matrices are calculated. A detailed description of the underlying geometric structures is also given and a generalization for restricting the motion to fundamental domains of H (three manifolds of constant negative sectional curvature) is outlined. Such models provide an interesting generalization to the known ones of multichannel scattering, quantum chaos and chaotic cosmology.