A New Mathematical Modeling of Maxwell Equations: Complex Linear Operator and Complex Field
Chein-Shan Liu

doi:10.3970/cmes.2008.038.025
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 38, No. 1, pp. 25-38, 2008
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Keywords Maxwell equations, Lorenz gauge condition, Wave equations, Jordan algebra, Complex operator, Complex field
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 {\it 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 {\it single} equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms of the$\unhbox \voidb@x \hbox {\boldmath$\gamma$}$-ring, we found that the Maxwell equations bear certain similarity with the Dirac equation. However, we also point out their differences.
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