Generally relativistical Tetrode-Weyl-Fock-Ivanenko formalism and behaviour of quantum-mechanical particles of spin 1/2 in the Abelian monopole field

Abstract

Some attention in the literature has been given to the case of a particle of spin 1/2 on the background of the external monopole potential. Some aspects of this problem are reexamined here. The primary technical novelty is that the tetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for describing a spinor particle is exploited. The choice of the formalism has turned out to be of great fruitfulness for examining the system. It is matter that, as known, the use of a special spherical tetrad in the theory of a spin 1/2 particle had led Schrodinger to a basis of remarkable features. The basis has been used with great efficiency by Pauli in his investigation on the pro- blem of allowed spherically symmetric wave functions in quantum mechanics. For our purposes, just several simple rules extracted from the much more com- prehensive Pauli's analysis will be quite sufficient; those are almost mnemo- nic working regulations. So, one may remember some very primary facts of D- functions theory and then produce automatically proper wave functions. It seems rather likely, that there may exist a generalized analog of such a re- presentation for J(i)-operators, that might be successfully used whenever in a linear problem there exists a spherical symmetry, irrespective of the con- crete embodiment of such a symmetry. In particular, the case of electron in the external Abelian monopole field completely come under the Sch-Pau method.