SOME PROBLEMS OF MATHEMATICAL PHYSICS IN POLYNUMBERS FIELD THEORY
2012jnq | Pavlov D.G., Kokarev S.S.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia; RSEC Logos, Yaroslavl, Russia, geom2004@mail.ru, logos-center@mail.ru

Some mathematical aspects of the invariant scalar operator Оn, that appears in polynumbers field theory, are considered together with some characteristic properties of its kernel. Concrete expressions for Berwald-Moor metrics and operator On in isotropic cylindrical, non-isotropic cylindrical and general spherical coordinate systems are derived in case n=3. Part of the results is expressed in terms of special functions, which are hyperbolic analogies of trigonometric ones, spherical harmonics and Legendre polynomials. General kind of radial part of n is calculated for arbitrary Оn. The problem of finding of hyperbolic field, generated by homogeneously charged hyperbolic sphere, is solved. We show, that there is no separable solutions to hyperbolic wave equation with cylindrical symmetry.

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