Fundamental Equations of Electromagnetics Using Field-Impulses as Physical Field-Integrators

As signified by the well-known Aharanov–Bohm effect, the fields only under-describe electromagnetics and are thus not sufficient, while the potentials over-describe electromagnetics and are more than necessary with gauge redundancy. In lieu of the traditional fields and potentials, this article presents new formulations that introduce from the outset the concept and utilization of field-impulses for the fundamental equations of electromagnetics. Unlike the potentials that may or may not be real or causal depending on the gauge, the field-impulses as physical field-integrators (time-integrals) are like fields being physically real, causal, and gauge-independent. Furthermore, the single electric field-impulse/integrator alone through its second-order (wave) equation is capable of aptly describing electromagnetics in all cases of electrostatics, magnetostatics, and electrodynamics. Upon close scrutiny and comparison, the optional static–dynamic decomposition of electric field-impulse can be related to the potentials with source-incorporated gauge condition. Such source-incorporated condition is unlike other popular gauge conditions that are source-free or incorporating the source implicitly. The electric field-impulse as physical field-integrator is necessary and sufficient for many aspects of electromagnetics including field derivation, Lorentz force, momentum, interaction energy, quantum particle–electromagnetic interactions, etc.