TY  - EJOU
AU  - Liu, Chein-Shan 

TI  - A New Mathematical Modeling of Maxwell Equations: Complex Linear Operator and Complex Field
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2008
VL  - 38
IS  - 1
SN  - 1526-1506

AB  - 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 <i>four</i> 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 <i>single</i> equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms of the &gamma;-ring, we found that the Maxwell equations bear certain similarity with the Dirac equation. However, we also point out their differences.
KW  - Maxwell equations
KW  -  Lorenz gauge condition
KW  -  Wave equations
KW  -  Jordan algebra
KW  -  Complex operator
KW  -  Complex field

DO  - 10.3970/cmes.2008.038.025