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Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

Southwest Research Institute, Space Science & Engineering, San Antonio, TX 78238, USA
Mathematics 2018, 6(7), 114; https://doi.org/10.3390/math6070114
Received: 14 May 2018 / Revised: 19 June 2018 / Accepted: 19 June 2018 / Published: 3 July 2018
Maxwell equations have two types of asymmetries between the electric and magnetic fields. The first asymmetry is the inhomogeneity induced by the absence of magnetic charge sources. The second asymmetry is due to parity. We show how both asymmetries are naturally resolved under an alternative formulation of Maxwell equations for fields or potentials that uses a compact complex vector operator representation. The developed complex symmetric operator formalism can be easily applied to performing the continuity equation, the field wave equations, the Maxwell equations for potentials, the gauge transformations, and the 4-momentum representation; in general, the developed formalism constitutes a simple way of unfolding the Maxwell theory. Finally, we provide insights for extending the presented analysis within the context of (i) bicomplex numbers and tessarine algebra; and (ii) Lp-spaces in nonlinear Maxwell equations. View Full-Text
Keywords: Maxwell equations; complex representation; E/M waves; gauge transformation; gravitomagnetism; Lp norms Maxwell equations; complex representation; E/M waves; gauge transformation; gravitomagnetism; Lp norms
MDPI and ACS Style

Livadiotis, G. Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials. Mathematics 2018, 6, 114. https://doi.org/10.3390/math6070114

AMA Style

Livadiotis G. Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials. Mathematics. 2018; 6(7):114. https://doi.org/10.3390/math6070114

Chicago/Turabian Style

Livadiotis, George. 2018. "Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials" Mathematics 6, no. 7: 114. https://doi.org/10.3390/math6070114

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