Three kinds of particles on a single rationally parameterized worldline

Vladimir V. Kassandrov; Nina V. Markova

doi:10.1134/s0202289316040101

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arXiv · 1702.02869

Three kinds of particles on a single rationally parameterized worldline

Vladimir V. Kassandrov·Nina V. Markova

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Abstract

We consider the light cone (`retardation') equation (LCE) of an inertially moving observer and a single worldline parameterized by arbitrary rational functions. Then a set of apparent copies, R- or C-particles, defined by the (real or complex conjugate) roots of the LCE will be detected by the observer. For any rational worldline the collective R-C dynamics is manifestly Lorentz-invariant and conservative; the latter property follows directly from the structure of Vieta formulas for the LCE roots. In particular, two Lorentz invariants, the square of total 4-momentum and total rest mass, are distinct and both integer-valued. Asymptotically, at large values of the observer's proper time, one distinguishes three types of the LCE roots and associated R-C particles, with specific locations and evolutions; each of three kinds of particles can assemble into compact large groups - clusters. Throughout the paper, we make no use of differential equations of motion, field equations, etc.: the collective R-C dynamics is purely algebraic

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Vladimir V. Kassandrov, Nina V. Markova. 2017-01-31. Three kinds of particles on a single rationally parameterized worldline. https://doi.org/10.1134/s0202289316040101

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