Collective Lorentz invariant dynamics on a single 'polynomial' worldline

Consider a worldline of a pointlike particle parameterized by polynomial functions, together with the light cone ('retardation') equation of an inertially moving observer. Then a set of apparent copies, R- or C-particles, defined by the (real or complex conjugate) roots of the retardation equation will be detected by the observer. We prove that for any 'polynomial' worldline the induced collective dynamics of R-C particles obeys a whole set of canonical conservation laws (for total momentum, angular momentum and the analogue of mechanical energy). Explicit formulas for the values of total angular momentum and the analogue of total rest energy (rest mass) are obtained; the latter is 'self-quantized', i.e. for any worldline takes only integer values. The dynamics is Lorentz invariant though different from the canonical relativistic mechanics. Asymptotically, at large values of the observer's proper time, the R-C particles couple and then assemble into compact incoming/outgoing clusters. As a whole, the evolution resembles the process of (either elastic or inelastic) scattering of a beam of composite particles. Throughout the paper the consideration is purely algebraic, with no resort to differential equations of motion, field equations, etc. © 2015 IOP Publishing Ltd.

Number of issue
39
Language
English
Status
Published
Number
395204
Volume
48
Year
2015
Organizations
  • 1 Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Moscow, Russian Federation
Keywords
conservation laws; formation of clusters; one-electron Universe; polynomial worldline; retardation equation; self-quantization
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/4511/