On the existence of maximizing curves for the charged-particle action
E. Minguzzi
Abstract
The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x0 and x1, with x1 in the chronological future of x0, and a ratio q/m, it is proved that a timelike connecting solution of the Lorentz force equation exists provided there is no null connecting geodesic and the spacetime is globally hyperbolic. As a result, the theorem answers affirmatively to the existence of timelike connecting solutions for the particular case of Minkowski spacetime. Moreover, it is proved that there is at least one C1 connecting curve that maximizes the functional I[γ]=∫γ ds+q/(mc2) ωover the set of C1 future-directed non-spacelike connecting curves.
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