%0 Journal Article
%T Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
%A Philippe Gravejat
%A Christian Hainzl
%A Mathieu Lewin
%A Eric S¨¦r¨¦
%J Physics
%D 2012
%I arXiv
%R 10.1007/s00205-012-0609-1
%X 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.
%U http://arxiv.org/abs/1204.2893v3