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Line and surface integrals in the hypercomplex numbers concept of Clifford algebra
2025-04-21
The article presents a generalization theory of functions of a complex variable for 3-dimensional Euclidean space and for Minkowski's space: Cauchy's integral theorem, Cauchy's integral formula, its integral representation for derivatives, and Stoker’s and Ostrogradsky-Gauss theorems. Also, line and surface integrals were combined and generalized within the framework of the concept of hypercomplex numbers. A bijection (one-to-one correspondence) was established between multidimensional vectors and hypercomplex numbers, i.e., the Pauli matrices (σi) for 3-dimensional Euclidean space and the Dirac matrices (γi) for Minkowski space were used as hypercomplex numbers and basis vectors. The results of the calculations were used to study the laws of physics; in particular, dual integration was applied – replacing surface integrals over “time” planes with integration over “purely spatial” planes. The law of conservation of 4-electromagnetic currents has been proven within the framework of the Clifford algebra concept.
Ссылка для цитирования:
Babaev A. K. 2025. Line and surface integrals in the hypercomplex numbers concept of Clifford algebra. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113520
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