The Electrodynamics of Continuous Electromagnetic Fields*

Electrodynamics is here formulated as a field theory rather than as a particle and field theory. Electromagnetic fields are taken to be continuous everywhere. Maxwell’s equations are assumed to be valid always, and second order calculus of variations is used to obtain fundamental equations from a covariant action in which the usual term involving particle mass m has been replaced by a term involving an integral over the covariant mass density µ associated with the fields.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 equations yield:

 • A covariant equation of motion for a charged body’s center of inertia (COI)

            Includes distortion of the body and radiation reaction

• Solutions of the Dirac and Schrodinger equations, which give mass density around the COI

            Mass densities for a body interacting with its environment, not probability densities

 • The electromagnetic mass of an interacting body consists of three parts: an interaction mass given by the Dirac or Schrodinger equation, an intrinsic mass co-located with charge, and an extrinsic (dark) mass outside the charged region

• Equations for the intrinsic electromagnetic fields co-located with charge density

• Stable shapes of charge densities having one sign. 

Electromagnetic interactions alone suffice to stabilize distributions of charge density having one sign.  All relevant properties can be calculated from the fields.