  In the development of the old ideas of Stueckelberg-Wheeler-Feynman on the
"one-electron Universe", we study the purely algebraic dynamics of the ensemble
of(two kinds of) identical point-like particles. These are represented by
the(real and complex conjugate) roots of a generic polynomial system of
equations that implicitly defines a single "worldline". The dynamics includes
events of "merging" of a pair of particles modelling the annihilation/creation
processes. Correlations in the location and motion of the particles-roots
relate, in particular, to the Vieta formulas. After a special choice of the
inertial-like reference frame, the linear Vieta formulas guarantee that, for
any worldline, the law of (non-relativistic) momentum conservation is
identically satisfied. Thus, the general structure of Newtonian mechanics
follows from the algebraic properties of a worldline alone. Some considerations
on relativization of the scheme are presented. A simple example of,
unexpectedly rich, "polynomial dynamics" is retraced in detail and illustrated
via an animation(available from ancillary file enclosed)
