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

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.

20 pages, 5 figures

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• Noncommutative analogue Aharonov-Bohm effect and superresonance
• Analogue Aharonov-Bohm effect in neo-Newtonian theory
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• Aharonov-Bohm Effect on Noncommutative Plane: A Coherent State Approach
• Aharonov-Bohm effect for a fermion field in a planar black hole "spacetime"
• Noncommutative Field Theory: Nonrelativistic Fermionic Field Coupled to the Chern-Simons Field in 2+1 Dimensions