Majorana Fermions in the Riemannian Space–Time and the Pauli Approximation

Abstract

Procedure of obtaining the non-relativistic Pauli equation from the Dirac theory is investigated in a covariant approach which is based on the use of an arbitrary basis in the bispinor space. The Pauli equation formally is written for a 4-component wave function. Due to the presence of an additional linear restriction on the bispinor wave function, the 4-component Pauli equation is equivalent to an equation for a 2-spinor. This covariant nonrelativistic approximation is applied to the theory of Majorana uncharged spin 1/2 particles, here again the Pauli theory is formulated in 4-component form which reduces to an equation for a 2-component complex spinor. In this context, the Dirac, Majorana and Pauli solutions with spherical symmetry are considered in detail.