Trajectories for Relativistic Particles in an Electromagnetic Field
We present a variational theory for the trajectories of a massive, charged particle in a relativistic spacetime with an electromagnetic field. We state some result on the existence and the multiplicity of such trajectories joining two points, assuming that the spacetime is standard stationary and the electromagnetic field is constant with respect to the standard time coordinate. The results are obtained using critical point theory for functionals on infinite dimensional manifolds and the topological properties of the spacetime.
KeywordsCritical Point Theory Lorentzian Manifold Timelike Curve Smooth Vector Field Lorentzian Geometry
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