Vladimir V. Kassandrov, Ildus Sh. Khasanov
In development of the old ideas of Stueckelberg-Wheeler-Feynman on "one-electron Universe", we study purely algebraic dynamics of (two kinds of) identical pointlike particles. These are represented by (real and complex conjugate) roots of a generic polynomial system of equations that implicitly defines a single "Worldline". The dynamics includes, in particular, events of "merging" of some two particles modelling the processes of annihilation/creation and the "exchange of quantum" as well. Correlations in the location and motion of the particles-roots relate, in particular, to the Vieta's formulas. After special choice of the inertial-like reference frame, the linear Vieta's formula ensures satisfaction of the law of (non-relativistic) momentum conservation and reproduces thus general structure of the Newtonian mechanics. Some considerations on relativization of the scheme are presented.
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http://arxiv.org/abs/1211.7002
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