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Trajectories for Relativistic Particles in an Electromagnetic Field

  • E. Caponio
  • A. Masiello
Conference paper

Abstract

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.

Keywords

Critical Point Theory Lorentzian Manifold Timelike Curve Smooth Vector Field Lorentzian Geometry 
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Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  • E. Caponio
    • 1
  • A. Masiello
    • 2
  1. 1.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly
  2. 2.Dipartimento di Matematica, Politecnico di BariBariItaly

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