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A New Mathematical Modeling of Maxwell Equations: Complex Linear Operator and Complex Field

Chein-Shan Liu1
1 Department of Civil Engineering, Taiwan University, Taipei, Taiwan

Computer Modeling in Engineering & Sciences 2008, 38(1), 25-38. https://doi.org/10.3970/cmes.2008.038.025

Abstract

In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms of the γ-ring, we found that the Maxwell equations bear certain similarity with the Dirac equation. However, we also point out their differences.

Keywords

Maxwell equations, Lorenz gauge condition, Wave equations, Jordan algebra, Complex operator, Complex field

Cite This Article

Liu, C. (2008). A New Mathematical Modeling of Maxwell Equations: Complex Linear Operator and Complex Field. CMES-Computer Modeling in Engineering & Sciences, 38(1), 25–38.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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