Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions

The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern-Simons solitons, or so-called anyons. The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. The electric charge and magnetic flux is (-q, -φ/Z) for one particle and (Zq, φ) for the other. When (Zq2/(h/2π)c)2<<1, and qφ/2π (h/2π)c takes on integer or half-integer values, the partial wave series is summed up approximately to give a closed form. The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level. (author)