Abstract
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/ℏc)2<<1, and qϕ/2πℏc 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.
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