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Quaternion Electromagnetism and the Relation with Two-Spinor Formalism

by In Ki Hong 1 and Choong Sun Kim 1,2,*
1
Department of Phyics and IPAP, Yonsei University, Seoul 03722, Korea
2
Institute of High Energy Physics, Dongshin University, Naju 58245, Korea
*
Author to whom correspondence should be addressed.
Universe 2019, 5(6), 135; https://doi.org/10.3390/universe5060135
Received: 26 April 2019 / Revised: 27 May 2019 / Accepted: 28 May 2019 / Published: 3 June 2019
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary “i” should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation. View Full-Text
Keywords: quaternion; electromagnetism; representation theory; Cayley-Dickson algebra; special relativity; twistor theory quaternion; electromagnetism; representation theory; Cayley-Dickson algebra; special relativity; twistor theory
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Hong, I.K.; Kim, C.S. Quaternion Electromagnetism and the Relation with Two-Spinor Formalism. Universe 2019, 5, 135.

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