The (2+12+1) curved Dirac equation in polar coordinates in the presence of electromagnetic field

In this work we study the covariant Dirac equation in (2+12+1) dimensional space–time in the presence of electromagnetic field. In polar coordinates, we show that by using a unitary transformation which implies a constraint between the components of gauge field, the covariant Dirac equation can be transformed into a Schrodinger-like differential equation for one of the spinor components. We also obtain the relativistic energy and spinor wave function for two different kinds of electrostatic potentials. The non-relativistic limit of the Dirac equation is also studied and it is shown that the upper spinor component satisfies the Pauli equation.