On the initial value formulation of classical electrodynamics

@article{Deckert2016OnTI,
  title={On the initial value formulation of classical electrodynamics},
  author={Dirk-Andr{\'e} Deckert and Vera Hartenstein},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2016},
  volume={49}
}
We describe a seemingly un-noticed feature of the text-book Maxwell–Lorentz system of classical electrodynamics which challenges its formulation in terms of an initial value problem. For point-charges, even after appropriate renormalization, we demonstrate that most of the generic initial data evolves to develop singularities in the electromagnetic fields along the light cones of the initial charge positions. We provide explicit formulas for the corresponding fields, demonstrate how this… 

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