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arXiv · 0708.3862

Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential

A. F. Ferrari·M. Gomes·C. A. Stechhahn
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Abstract

In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in $2 + 1$ dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the \textit{commutative} Aharonov-Bohm problem. We calculate, in this setting, the scattering amplitude and the corrections to the differential and total cross sections for a spin 1/2 particle, in the small-flux limit.

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A. F. Ferrari, M. Gomes, C. A. Stechhahn. 2007-08-28. Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential. https://doi.org/10.1103/physrevd.76.085008

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