2010/09/16 by Gernot Bauer, Bauer, G., Dirk-André Deckert +3 · 2 citations
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1009.3103
We study the equations of Wheeler-Feynman electrodynamics which is an action-at-a-distance theory about world-lines of charges that interact through their corresponding advanced and retarded Liénard-Wiechert field terms. The equations are non-linear, neutral, and involve time-like advanced as well as retarded arguments of unbounded delay. Using a reformulation in terms of Maxwell-Lorentz electrodynamics without self-interaction, which we have introduced in a preceding work, we are able to establish the existence of conditional solutions. These are solutions that solve the Wheeler-Feynman 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 trajectories.