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ISSN 2071-0186   Ukr. J. Phys. 2015, Vol. 60, N 5, p.468-477
doi:10.15407/ujpe60.05.0468   Paper

Khoroshkov Yu.V.

4, Petrovs’kyi Str., apt. 40, Kyiv 03087, Ukraine
(e-mail: YuriHoroshkov@gmail.com)

Mirror Symmetry As A Basis For Constructing A Space-Time Continuum

Section: General problems of theoretical physics
Language: English

Abstract: By mirroring a one-dimensional oriented set in a complex space specially created on the basis of a symmetry, a mirror n-dimensional space with n > 1 has been constructed. The geometry of the resulting space is described by the Clifford algebra. On the basis of the algebra of hyperbolic hypercomplex numbers, a pseudo-Euclidean space has been constructed with the metric of the Minkowski space. The conditions for a function of a hyperbolic hypercomplex argument to be analytic (h-analyticity) are obtained. The conditions implicitly contain the Maxwell equations for the 4-potential in a free space.

Key words: mirror transformation, Clifford algebra, hyperbolic hypercomplex numbers, Minkowski space.