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Mini-workshop on "Mathematical challenges in Quantum Electrodynamics"
Organizers: Jan Derezinski (Warsaw), Paul Indelicato (CNRS), Krzysztof Pachucki (Warsaw)


Eric Séré (Paris, France): "The self-consistent Dirac vacuum in classical electromagnetic fields"
Monday 29 April 2013, 11:20 - 12:20
Amphi Hermite


Eric Séré
Paris, France
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"The self-consistent Dirac vacuum in classical electromagnetic fields."

Abstract: This is joint work with Christian Hainzl, Philippe Gravejat and Mathieu Lewin. 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.