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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2013

Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Résumé

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 nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.
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Dates et versions

hal-00687272 , version 1 (12-04-2012)
hal-00687272 , version 2 (03-05-2012)
hal-00687272 , version 3 (11-12-2012)

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Philippe Gravejat, Christian Hainzl, Mathieu Lewin, Eric Séré. Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields. Archive for Rational Mechanics and Analysis, 2013, 208 (2), pp.603-665. ⟨10.1007/s00205-012-0609-1⟩. ⟨hal-00687272v3⟩
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