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