Nonlinear Phenomena in Complex Systems, 2016, Vol.19, No.4, pp.330-344

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2016, Vol.19, No.4, pp.330-344

Majorana Fermions in the Riemannian Space–Time and the Pauli Approximation
V. V. Gilewsky and V. M. Red’kov

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.

Key words: spin 1/2, Dirac and Majorana particles, Lorentz symmetry, Pauli approximation, spherical symmetry

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