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 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 ε. 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. 85 (2012) 041701(R)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.