English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recent results on the maximization of the charged-particle action I in aglobally hyperbolic spacetime are discussed and generalized. We focus on themaximization of I over a given causal homotopy class C of curves connecting twocausally related events x_0 <= x_1. Action I is proved to admit a maximum on C,and also one in the adherence of each timelike homotopy class. Moreover, themaximum on C is timelike if C contains a timelike curve (and the degree ofdifferentiability of all the elements is at least C^2).  In particular, this last result yields a complete Avez-Seifert type solutionto the problem of connectedness through trajectories of charged particles in aglobally hyperbolic spacetime endowed with an exact electromagnetic field:fixed any charge-to-mass ratio q/m, any two chronologically related events x_0<< x_1 can be connected by means of a timelike solution of the Lorentz forceequation (LFE) corresponding to q/m. The accuracy of the approach is stressedby many examples, including an explicit counterexample (valid for all q/m) inthe non-exact case.  As a relevant previous step, new properties of the causal path space, causalhomotopy classes and cut points on lightlike geodesics are studied.Comment: 24 pages, no figure

Connecting Solutions of the Lorentz Force Equation do Exist