АЛГЕБРАИЧЕСКИЕ ОСНОВАНИЯ МЕХАНИКИ НЬЮТОНА: ЗАКОНЫ СОХРАНЕНИЯ, ИНДУЦИРОВАННЫЕ ПОЛИНОМИАЛЬНЫМИ СВЯЗЯМИ

In development of the old ideas of Stueckelberg-Wheeler-Feynman on “one-electron Universe”, we define trajectories of motions of the ensemble of (two kinds of) identical point-like particles by the algebraic system of implicit equations. We choose the polynomial form of the functions which define a single “worldline” and represent by their roots (real and complex conjugate) a model for dynamics of particles. The dynamics includes events of “merging” of some two particles modelling the processes of annihilation/creation. Correlations in the location and motion of the particles-roots relate, in particular, to the Vieta's formulas. Analyzing these relations we found that this algebraic construction reproduces by itself the general structure of Newtonian mechanics including almost the complete set of the canonical conservation laws.