ALGEBRA, GEOMETRY AND PHYSICS OF DOUBLE NUMBERS
2013jfz | 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

The paper presents developed version of talk, given at the seminar, which took place 04.04.2013 in PFUR (Moscow) with sir R. Penrose. Some important analogies of complex algebra and analysis based on double numbers algebra are considered (polar and exponential forms of double numbers, elementary functions over double numbers, linearfractional transformations and hyperbolic spinors, h-holomorphic functions and their properties, h-holomorphic extensions). The second part of the paper is devoted to some physical applications of double numbers algebra (SR and its conformal generalization, the «theory of everything» in Hyperland, extravariational principle). The theory of Hyperland can be treated as low-dimensional version of future more realistic «theory of everything», based on polynumbers algebra Pn.

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