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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022 Volume 206, Pages 35–41 (Mi into963)

The law of conservation of electric charge and the physical interpretation of the generalized Cauchy–Riemann system

Yu. A. Gladyshev, E. A. Loshkareva

Tsiolkovsky Kaluga State University

Abstract: In this paper, we continue the study of generalizations of the Cauchy–Riemann (CR) conditions obtained earlier, which, under certain assumptions, can be interpreted as Maxwell's equations of electromagnetic field. The main mathematical tools used in the work is the technique of two quaternion variables. This work does not contain any physical statements, but is a theoretical analysis that can be carried out for systems of generalized CR conditions.

Keywords: quaternion, spinor, Cauchy–Riemann system, Laplace equation, Maxwell system, law of conservation of electric charge.

UDC: 511.84

MSC: 46S05, 47S05

DOI: 10.36535/0233-6723-2022-206-35-41



© Steklov Math. Inst. of RAS, 2025