General Solutions of Relativistic Wave Equations

Abstract

General solutions of relativistic wave equations are studied in terms of functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is established. A generalization of the Gel'fand-Yaglom theory for higher-spin equations is given. A two-dimensional complex sphere is associated with each point of Minkowski spacetime. The separation of variables in a general relativistically invariant system is obtained via the hyperspherical functions defined on the surface of the two-dimensional complex sphere. In virtue of this the wave functions are represented in the form of series in hyperspherical functions. Such a description allows one to consider all the physical fields on an equal footing. General solutions of the Dirac and Weyl equations, and also the Maxwell equations in the Majorana-Oppenheimer form, are given in terms of functions on the Lorentz group.