DIRAC – KAHLER PARTICLE IN THE LOBACHEVSKY SPACE, NON-RELATIVISTIC APPROXIMATION, BOSON INTERPRETATION

Abstract

The article is concerned with constructing the exact solutions for the Dirac – Kahler wave equation in the non-relativistic approximation for the simplest non-Euclidean geometrical model – hyperbolic Lobachevsky space. For the minimum value of the conserved angular momentum j = 0, the radial equations reduce to those solved in the elementary function. For greater values j = 1, 2, 3, ...,  the radial equations reduce to a couple of the four-order differential equations that are solved with the help of the factorization method. The general solution to each four-order order equation, involving four fundamental solutions, is constructed. The obtained solutions of the Dirac – Kahler wave equation cannot be solved in terms of the Pauli solutions on the background of Lobachevsky space, therefore any fermion interpretation for the Dirac – Kahler particle cannot be used.