Charged fermion in two-dimensional curved spaces of constant Gaussian curvature with constant magnetic flux

Abstract

We investigate the behavior of spin-1/2 particles (electron and positron) confined to the Gaussian curvature surfaces. For the non-negative Gaussian curvatures, we present the preliminary results in cylindrical and spherical cases. To be specific we use the deformed hyperbolic solutions to obtain eigenvalues of the Dirac equation in the presence of an axial gauge field. Our results demonstrate the quantized energy and eigenstates of fermion. The quantization of energy depends on the spin-orbit coupling and the Landau quantization. The imaginary energy is obtained from the negative Gaussian curvatures. It is interpreted as the quasi normal mode (QNM). The angular momentum of fermion is shifted by addition of the constant magnetic flux. The fermion behaves like boson when the flux is half-integer.