finsler geometry, hypercomplex numbers and physics
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FIELD AND PARTICLELIKE STRUCTURES ON A UNIQUE WORLD LINE
2016jfw | V.V. Kassandrov  // Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, Moscow, Russia, vkassan@sci.pfu.edu.ru

We present a review of works on the algebraic realization of the “one-electron Universe” concept of Stueckelberg-Wheeler-Feynman. Two different mechanisms of “multiplication” of copies-particles on a unique World line (WL) are proposed: implicit definition of a WL by a system of algebraic equations and the light cone equation (LCE) in the process of detection by an external observer. In both cases, for polynomial and/or rational parameterization of a WL, there arises the correlated dynamics of two kinds of particles corresponding to real (R-) or complex congugate (C-) roots of polynomial equations. As a direct consequence of the Vieta’s formulas, this dynamics turns out to be conservative: for the set of RC- particles the laws of conservation of total momentum, angular momentum and (the analogue of) total energy do hold. Satisfaction of the Newton’s laws and generation of mass of an arbitrary value for a system of two macroscopic bodies are established. In the model based on the LCE the collective RC-dynamics is Lorentz-invariant, and the total rest mass is necessarily integer-valued. At great values of the observer’s proper time, the effect of “coupling” of RC-particles takes place and, under specific conditions, – the effect of clusterization of pairs. In the case of à rationally parameterized WL, three distinct types of RC-particles with specific localization and dynamics can be asymptotically distinguished.



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