Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

@article{Gravejat2013ConstructionOT,
  title={Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields},
  author={Philippe Gravejat and Christian Hainzl and Mathieu Lewin and {\'E}ric S{\'e}r{\'e}},
  journal={Archive for Rational Mechanics and Analysis},
  year={2013},
  volume={208},
  pages={603-665}
}
Using the Pauli–Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac’s vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are… 
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