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Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials

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  • George Livadiotis

    (Southwest Research Institute, Space Science & Engineering, San Antonio, TX 78238, USA)

Abstract

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) L p -spaces in nonlinear Maxwell equations.

Suggested Citation

  • George Livadiotis, 2018. "Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials," Mathematics, MDPI, vol. 6(7), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:114-:d:155848
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    References listed on IDEAS

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    1. Livadiotis, George, 2007. "Approach to general methods for fitting and their sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 518-536.
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