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

Abstract

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $\kappa$-Poincaré-Hopf algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\epsilon$. 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.

12 pages, no figures, submitted for publication

References in corpus (2)

• Aharonov-Bohm-Casher Problem with a nonminimal Lorentz-violating coupling
• Fock space, quantum fields and kappa-Poincaré symmetries

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