General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

Details General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

2005-03-25

arxiv.org/abs/math-ph/0503058v2

Int.J.Theor.Phys.46:741-805,2007

Physics

Mathematical Physics

56 pages, LaTeX2e

Scientific paper

10.1007/s10773-006-9077-4

A construction of relativistic wave equations on the homogeneous spaces of the Poincar\'{e} group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski spacetime and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincar\'{e} and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere.

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