Potentials in the Algebraic Scattering Theory
The algebraic scattering theory (AST) allows a completely algebraic determination of the S-matrix for scattering systems with a given dynamical symmetry [1, 2]. Of particular interest for practical applications is the AST with SO(1, 3) or SO(2, 3) dynamical symmetry, since the S-matrix for Coulomb scattering appears as a special case of the more general, algebraically derived S-matrices. In an earlier contribution  we showed that the algebraic S-matrix is not unique, but comprises two different classes of S-matrices with algebraically undetermined phase factors. Since in the algebraic formalism the scattering potentials do not appear explicitly, the question naturally arises, how potentials corresponding to a given symmetry can be constructed. In the following, this problem is solved for the case of an SO(1, 3) and an SO(2, 3) dynamical symmetry.