An Exploration of Electrodynamics, Quantum Mechanics, and Particle Physics without Point Particles

The mathematical journey from electrodynamics to solutions for quantum mechanics and perhaps particle physics is lengthy but straightforward. Assuming that the electromagnetic fields are continuous eliminates point charges but requires reformulation of other physical theory. Second-order calculus of variations obtains fundamental equations from a covariant action in which the usual term involving particle mass m has been replaced by a term involving an integral over the covariant mass density µ associated with the fields. These fundamental equations yield a covariant equation of motion for a charged body’s center of inertia provided the momentum of the system is accounted for, and solutions for the Dirac and Schrodinger equations for a body interacting with an exterior field. The mass of a charged body is shown to be partitioned into interaction, intrinsic, and extrinsic masses. If body momentum is self-contained, then the fundamental equations can give equations describing charged bodies surrounded by equipotentials and stabilized by their electromagnetic self-fields. Body properties can be calculated from the fields.