A path to calculating the masses, charges and other properties of fundamental particles

We present a family of field theories extending electromagnetic field theory. In place of matter fields, such as point charges or spinor fields, we demonstrate that Lagrangian terms that are higher order in differentiation of the electromagnetic field tensor can provide a balance for the divergence of the electromagnetic field tensor inside of objects, allowing for the admittance of electric charge.

Without assuming any prior structure, we solve the field equations for the simplest theory (which includes gravity) in spherical coordinates. There is only one solution, found numerically, with mass and charge fixed by the fundamental constants of the theory, where the charge is 0 to within the numerical accuracy of the calculation: the field theory only allows for a single spherical (spin-0) particle, with quantized mass and apparently zero charge.

This provides a potential path to calculating the mass, charge, and other properties of fundamental objects, without requiring prior structure such as particles, strings, etc. This is the first time the author is aware of this being achieved by a field theory.

Other forces outside of gravity and electromagnetism arise from the Lagrangian, which are all short-range, in that their influence, while strong near the center of the spherical object, decay much faster than electromagnetic force, as one moves from the center. Some of these short-range forces change sign under a parity transformation.