Dirac equation with external potential and initial data on Cauchy surfaces

@article{Deckert2014DiracEW,
  title={Dirac equation with external potential and initial data on Cauchy surfaces},
  author={Dirk-Andr{\'e} Deckert and Franz Merkl},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={122305}
}
With this paper, we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincare group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove… 

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