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 “oneelectron Universe”
concept of StueckelbergWheelerFeynman. Two different mechanisms of “multiplication”
of copiesparticles 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 RCdynamics is
Lorentzinvariant, and the total rest mass is necessarily integervalued. At great values
of the observer’s proper time, the effect of “coupling” of RCparticles takes place and,
under specific conditions, – the effect of clusterization of pairs. In the case of à rationally
parameterized WL, three distinct types of RCparticles with specific localization and
dynamics can be asymptotically distinguished.
