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On the formulation of initial-value problems for systems consisting of relativistic particles

Abstract

We discuss questions related to the well-posedness of problems on the motion of relativistic many-body systems. For one-dimensional relativistic motion of N similar charges, we prove that an ordinary Cauchy problem usual in Newton mechanics can be stated; this is done in the framework of microscopic Maxwell-Lorentz electrodynamics (including a model with self-action) or Wheeler-Feynman theory.

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

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Kirpichev, S.B., Polyakov, P.A. On the formulation of initial-value problems for systems consisting of relativistic particles. J Math Sci 141, 1051–1061 (2007). https://doi.org/10.1007/s10958-007-0032-6

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Keywords

  • Cauchy Problem
  • Circular Orbit
  • Central Collision
  • Classical Electrodynamic
  • Advanced Potential