Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $κ$-Poincaré-Hopf algebra. We consider the nonrelativistic limit of the $κ$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.

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