Physical theories in hypercomplex geometric description

Compact description is given of algebras of poly-numbers: quaternions, bi-quaternions, double (split-complex) and dual numbers. All units of these (and exceptional) algebras are shown to be represented by direct products of 2D vectors of a local basis defined on a fundamental surface. In this math medium a series of equalities identical or similar to known formulas of physical laws is discovered. In particular, a condition of the algebras' stability with respect to transformations of the 2D-basis turns out equivalent to the spinor (Schrödinger-Pauli and Hamilton-Jacobi) equations of mechanics. It is also demonstrated that isomorphism of SO(3, 1) and SO(3, ℂ) groups leads to formulation of a quaternion relativity theory predicting all effects of special relativity but simplifying solutions of relativistic problems in non-inertial frames. Finely it is shown that the Cauchy-Riemann type equations written for functions of quaternion variable repeat vacuum Maxwell equations of electrodynamics, while a quaternion space with non-metricity comprises main relations of Yang-Mills field theory. © 2014 World Scientific Publishing Company.

Авторы
Редакторы
-
Издательство
-
Номер выпуска
6
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
1450062
Том
11
Год
2014
Организации
  • 1 Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Miklukho-Maklaya, Str. 6, Moscow 117198, Russian Federation
Ключевые слова
electrodynamics; fundamental surface; Hypercomplex numbers; quantum and classical mechanics; quaternions; spinors; theory of relativity; Yang-Mills field
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4875/