The Dirac equation in orthogonal coordinate systems. I. The local representation

Abstract

A new approach to handle the Dirac equation in orthogonal curvilinear coordinate systems is presented. It is applicable at least for all coordinate systems which can be described by conformal mappings in a specified manner. The method is based on a space-dependent transformation of the wavefunction corresponding to a space-dependent set of Dirac matrices, a local representation. This transformation, which can be given in closed form, is chosen in such a way that the Dirac equation in the given coordinates assumes a very simple form, well suited for numerical and analytical examinations. The relationship between the different forms of the Dirac equation is then discussed. The special case of spherical coordinates is investigated in detail.