Conservative Relativistic Algebrodynamics Induced on an Implicitly Defined World Line

Abstract

In the framework of the Stueckelberg-Wheeler-Feynman concept of a “one-electron Universe” we consider a world line implicitly defined by a system of algebraic (precisely, polynomial) equations. A collection of pointlike “particles” of two kinds on the world line (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and is detected then by an external inertial observer through light cone connections. Then the observed collective dynamics of the particle ensemble is, generally, subject to a number of Lorentz-invariant conservation laws. Remarkably, this property follows from the Vieta formulas for roots of the generating polynomial system. At some discrete instants of the observer’s proper time, mergers and subsequent transmutations of a pair of particles-roots take place, thus simulating the processes of annihilation/creation of a particle/antiparticle pair.