Abstract
Wheeler–Feynman electrodynamics (WF) is an action-at-a-distance theory about world-lines of charges that in contrary to the textbook formulation of classical electrodynamics is free of ultraviolet singularities and is capable of explaining the irreversible nature of radiation. In WF, the world-lines of charges obey the so-called Fokker–Schwarzschild–Tetrode (FST) equations, a coupled set of nonlinear and neutral differential equations that involve time-like advanced as well as retarded arguments of unbounded delay. Using a reformulation of this theory in terms of Maxwell–Lorentz electrodynamics without self-interaction that we have introduced in a preceding work, we are able to establish the existence of conditional solutions. These conditional solutions solve the FST equations on any finite time interval with prescribed continuations outside of this interval. As a byproduct, we also prove existence and uniqueness of solutions to the Synge equations on the time half-line for a given history of charge world-lines.
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Bauer, G., Deckert, D.A. & Dürr, D. On the existence of dynamics in Wheeler–Feynman electromagnetism. Z. Angew. Math. Phys. 64, 1087–1124 (2013). https://doi.org/10.1007/s00033-012-0293-x
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DOI: https://doi.org/10.1007/s00033-012-0293-x