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

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

2007-08-28

arxiv.org/abs/0708.3862v1

Phys.Rev.D76:085008,2007

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.76.085008

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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