Normed Division Algebras Application to the Monopole Physics
Keywords:Levi-Civita transformation, harmonic oscillator, MICZ-Kepler problem, duality, Dirac, Yang, and SO(8) monopoles, nine-dimensional space, octonion
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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