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The Dual Continuity Equations
Version 1
: Received: 18 August 2018 / Approved: 19 August 2018 / Online: 19 August 2018 (05:03:06 CEST)
A peer-reviewed article of this Preprint also exists.
Arbab, A.I.; Alsaawi, N.N. The Dual Continuity Equations. Optik 2021, 248, 168095, doi:10.1016/j.ijleo.2021.168095. Arbab, A.I.; Alsaawi, N.N. The Dual Continuity Equations. Optik 2021, 248, 168095, doi:10.1016/j.ijleo.2021.168095.
Abstract
The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.
Keywords
continuity equation; Maxwell equations: massive electrodynamics; London's superconductivity; proca-Maxwell equations; duality transformations
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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