Physics – Mathematical Physics
Scientific paper
2005-05-05
Commun.Math.Phys. 264 (2006) 349-370
Physics
Mathematical Physics
24 pages, no figures
Scientific paper
10.1007/s00220-006-1547-2
Recent results on the maximization of the charged-particle action I in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I over a given causal homotopy class C of curves connecting two causally 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, the maximum on C is timelike if C contains a timelike curve (and the degree of differentiability of all the elements is at least C^2). In particular, this last result yields a complete Avez-Seifert type solution to the problem of connectedness through trajectories of charged particles in a globally 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 force equation (LFE) corresponding to q/m. The accuracy of the approach is stressed by many examples, including an explicit counterexample (valid for all q/m) in the non-exact case. As a relevant previous step, new properties of the causal path space, causal homotopy classes and cut points on lightlike geodesics are studied.
Minguzzi Ettore
Sánchez Miguel
No associations
LandOfFree
Connecting solutions of the Lorentz force equation do exist does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Connecting solutions of the Lorentz force equation do exist, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connecting solutions of the Lorentz force equation do exist will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114230