The dual continuity equations

The ordinary continuity equation relating to 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 longitudinal and transverse currents and the densities associated with them are found to be coupled with each other. Each of these quantities is found to obey a wave equation traveling at the velocity of light in a vacuum. London equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London equations are symmetric and are shown to be dual to each other. It is shown that London’s equations are Maxwell’s equations with a 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. •A system of dual continuity equations involving longitudinal and transverse currents is introduced.•Symmetric London’s equations of superconductivity are derived.•It is shown that London’s equations of superconductivity are forms of continuity equations.•A symmetric Lorentz force on a moving charge is derived.