Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations

@article{Arminjon2011EquivalentFO,
  title={Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations},
  author={Mayeul Arminjon and Frank Reifler},
  journal={Brazilian Journal of Physics},
  year={2011},
  volume={43},
  pages={64-77}
}
One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved space-time. This canonical form is needed… 

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