Normed Division Algebras Application to the Monopole Physics

Dai-Nam Le; Van-Hoang Le

doi:10.15625/0868-3166/15905

Author affiliations

Authors

Dai-Nam Le \(^1\)Department of Theoretical Physics, Faculty of Physics and Engineering Physics, University of Science, Ho Chi Minh City, Vietnam, 227 Nguyen Van Cu Street, District 5, Ho Chi Minh City, Vietnam;
\(^2\)Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam;
\(^3\)Atomic Molecular and Optical Physics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
\(^4\)Faculty of Applied Sciences, Ton Duc Thang University, 19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam
Van-Hoang Le Ho Chi Minh City University of Education http://orcid.org/0000-0003-4027-0729

DOI:

https://doi.org/10.15625/0868-3166/15905

Keywords:

Levi-Civita transformation, harmonic oscillator, MICZ-Kepler problem, duality, Dirac, Yang, and SO(8) monopoles, nine-dimensional space, octonion

Abstract

We review some normed division algebras (R, C, H, O) applications to the monopole physics and MICZ-Kepler problems. More specifically, we will briefly review some results in applying the normed division algebras to interpret the existence of Dirac, Yang, and SO(8) monopoles. These monopoles also appear during the examination of the duality between isotropic harmonic oscillators and the MICZ-Kepler problems. We also revisit some of our newest results in the nine-dimensional MICZ-Kepler problem using the generalized Hurwitz transformation.

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