Imaginary magnetic field in relativistic quantum mechanics

An important equation in relativistic quantum mechanics is Dirac's equation, which replaces the Schrödinger equation which is not Lorentz invariant. In this work the non-selfadjoint Dirac operator D_a on circle with a complex magnetic field will be investigated. We will find out under which conditions this operator will be normal and under which conditions it will be quasi-self-adjoint. Its spectrum and eigenvectors will be found. We will prove that the eigenvectors of the quasi-self-adjoint Dirac operator D_a form a Riesz basis, but do not form a Bari basis.