Abstract
We study the nonrelativistic limit of the quantum theory of a Chern–Simons field minimally coupled to a scalar field with quartic self-interaction. The renormalization of the relativistic model, in the Coulomb gauge, is discussed. We employ a procedure to calculate scattering amplitudes for low momenta that generates their |p|/m expansion and separates the contributions coming from high and low energy intermediary states. The two-body scattering amplitude is calculated up to order p2/m2. It is shown that the existence of a critical value of the self-interaction parameter for which the two-particle scattering amplitude reduces to the Aharonov–Bohm one is a strictly nonrelativistic feature. The subdominant terms correspond to relativistic corrections to the Aharonov–Bohm scattering. A nonrelativistic reduction scheme and an effective nonrelativistic Lagrangian to account for the relativistic corrections are proposed.
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