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Noncommutative Correction to the Aharonov-Bohm Scattering: a Field Theory Approach

M. A. Anacleto·M. Gomes·A. J. da Silva·D. Spehler
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Abstract

We study a noncommutative nonrelativistic theory in 2+1 dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalizability of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For small noncommutativity we fix the corrections to the Aharonov-Bohm scattering and prove that up to one-loop the model is free from dangerous infrared/ultraviolet divergences.

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M. A. Anacleto, M. Gomes, A. J. da Silva, D. Spehler. 2004-07-15. Noncommutative Correction to the Aharonov-Bohm Scattering: a Field Theory Approach. https://doi.org/10.1103/physrevd.70.085005%2010.1103%2Fphysrevd.70.089903%2010.1103%2Fphysrevd.70.129905

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