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arXiv · hep-th/9801192

Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering

M. Gomes·J. M. C. Malbouisson·A. J. da Silva
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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 $p^2/m^2$. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-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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M. Gomes, J. M. C. Malbouisson, A. J. da Silva. 1998-01-28. Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering. https://doi.org/10.1142/s0217751x98001566

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