Geodesic
On gauge transformations of electromagnetic potentials in the quaternion form
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 50-56.

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In this paper, we generalize the Cauchy–Riemann equations of the theory of functions of a complex variable to quaternion functions of eight variables and indicate that some properties of functions of a complex variable remain valid in this case. We propose an interpretation of the system obtained as the system of electrodynamic Maxwell equations and introduce electromagnetic potentials in the quaternionic form. From these general positions, we also introduce gauge transformations and obtain their specific forms.
Mots-clés : quaternion
Keywords: gauge transformation, Cauchy–Riemann system, Maxwell equations. 
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Yu. A. Gladyshev. On gauge transformations of electromagnetic potentials in the quaternion form. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Tome 190 (2021), pp. 50-56. http://geodesic.mathdoc.fr/item/INTO_2021_190_a4/

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