Mathematics Colloquia and Seminars

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To this day a physically meaningful and mathematically rigorous theory of relativistic interaction of charges is lacking. I will explain the basic obstacle in field theories, the so-called self-interaction, which leads to ill-defined equations of motion, and discuss the only known candidate for classical electrodynamics, namely Wheeler-Feynman (WF) electrodynamics, which is able to describe radiation damping without a self-interaction mechanism. Though the fundamental equations of WF electrodynamics are free of singularities, the question of existence and uniqueness of solutions is completely open for over 40 years. The mathematical difficulty arises from terms in the WF equations that have time-like advanced and retarded arguments of state-dependent delay. Those terms render notions like local solutions meaningless, and therefore, cannot be treated by standard techniques. I will report on present results and recent progress in this field.