2002/09/19 by V. V. Varlamov
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #physics.comp-ph #quant-ph #msc:22E43 #msc:35Q40 #msc:22E70 #msc:33C70
published as Int.J.Theor.Phys. 42 (2003) 583-633 · 47 pages, LaTeX2e
arxiv created 2002/09/19 · arxiv updated 2009/11/30
General solutions of relativistic wave equations are studied in terms of the 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 formalism for higher-spin equations is given. It is shown that a two-dimensional complex sphere is associated with the 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 on the hyperspherical functions. Such a description allows 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 the functions on the Lorentz group.