On the existence of maximizing curves for the charged-particle action

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 x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, 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^{1} connecting curve that maximizes the functional I[γ]=\int_γ ds+q/(mc^2) ωover the set of C^{1} future-directed non-spacelike connecting curves.

AMSLatex, 6 pages

Cited by in corpus (4)

• Eisenhart's theorem and the causal simplicity of Eisenhart's spacetime
• Causality of spacetimes admitting a parallel null vector and weak KAM theory
• Comment on ``The Avez-Seifert theorem for the relativistic Lorentz force equation'' and other related works
• Maximizing curves for the charged-particle action in globally hyperbolic spacetimes