On the Existence of Maximizing Curves for the Charged-particle Action
نویسندگان
چکیده
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 C connecting curve that maximizes the functional I[γ] = ∫ γ ds + q/(mc)ω over the set of C future-directed non-spacelike connecting curves.
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