Geometry and physics of holomorphic functions in polynumbers field theory
2013jgz | 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

A physical-geometric interpreting of holomorphic functions over polynumbers variable for a number of holomorphicity classes is investigated with using tangent construction, developed in [5]. It is shown, that any concrete choice of holomorphic function (polynumber potential) defines some field-theoretical model with background space-time of GR together with tensor fields of a various ranges. The question on local causal structure of pseudoRiemannian space-time, obtained by tangent construction in Berwald-Moor space, is investigated in general form. It is shown, that the only two causal types of space-times with signature(+,−, −,−) and(+,+,−,−) can be generated by tangent construction. The systems of differential equations, defining polynumber potential for Schwarzschild metric and cosmological FRW-metrics are derived.

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