Variational methods in relativistic quantum mechanics

@article{Esteban2007VariationalMI,
  title={Variational methods in relativistic quantum mechanics},
  author={Maria J. Esteban and Mathieu Lewin and Eric S'er'e},
  journal={Bulletin of the American Mathematical Society},
  year={2007},
  volume={45},
  pages={535-593}
}
  • Maria J. Esteban, Mathieu Lewin, Eric S'er'e
  • Published 2007
  • Physics, Mathematics
  • Bulletin of the American Mathematical Society
  • This review is devoted to the study of stationary solutions of lin- ear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy func- tional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below. This has two main consequences. First, the energy functional is strongly indefinite… CONTINUE READING

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