Interaction between Elementary Particles. Part I

An elementary particle is considered as a mathematical point which under an invariant law of communication involving a universal length $a$ establishes a primary potential in space-time. Due to the peculiar communication law, $r^2+c^2{t}^2+a^2=0\mathrm{}$ or $S^2=0\mathrm{}$, in contrast to the light signal law $R^2=0\mathrm{}$, the primary potential is without singularity at $r=0\mathrm{}$. It becomes the background of a regular electrodynamic or mesonic field and automatically yields a finite radius $a$ to the charge distribution, with a density falling off as ${\left(\frac{a}{r}\right)}^5$ at larger distances. The potentials of different particles are additive so that all quantities obey the super-position law. The total force on the Nth particle is produced under the same invariant communication law $S=0\mathrm{}$ by integration of the force density $k_N$ over the volume elements of the instantaneous rest system. $K_N$ is the resultant of mutual and self-forces, $K_N=S_M{K}_{\mathrm{MN}}$. Only retarded field interaction is admitted between different particles. The original production of the self-charge by the center and its force reaction on the center is derived from a heuristic scheme involving half-retarded, half-advanced potentials, as a substitute for the instantaneous reaction between the "parts" of a charge. In the dynamics of the particle a variable "acceleration mass" of field origin is added to the mechanical mass. An experimental determination of mass differences under various very high accelerations could reveal the unknown ratio between the field mass and the mechanical mass of a charged particle.