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General solutions of relativistic wave equations. (English) Zbl 1027.83003
The starting point of the paper is a criticism of the plane-wave solutions of the relativistic wave equations. As an improvement, the author presents these solutions in the form of series of hyperspherical functions. His theory is based on the isomorphism \(SL(2,\mathbb{C})\sim\) complex \(SU(2)\), and a generalization of the Gel’fand-Yaglom formalism. The technique of separating the variables is applicable since hyperspherical functions are defined on a two-dimensional complex sphere. Consequently, several fields are described in terms of functions on the Lorentz group.
In the last sections of the paper it is shown how the Dirac, Weyl and Maxwell equations can be considered particular cases of a general relativistically invariant system.

MSC:
83A05 Special relativity
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
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