Two effective models for the Dirac vacuum in electromagnetic fields
The authors here gather results they exposed in an already published paper and in a preprint deposited in HAL. They analyze the models of Pauli-Villars and Euler-Heisenberg which describe the effects of the polarization of Dirac void on the electromagnetic fields which occur there. They first recall how to recover the model of Pauli-Villars starting from an Hamiltonian which acts on the Fock fermionic space. The authors recall the results they obtained in [Arch. Ration. Mech. Anal. 208, No. 2, 603--665 (2013; Zbl 1269.81202)] which prove that the energy of Pauli-Villars may be built from an electromagnetic potential \(A\in L^{1}(\mathbb{R}^{3})^{4}\cap \overset{.}{H}^{1}(\mathbb{R}^{3})\times \overset{.}{H}_{\mathrm{div}}^{1}( \mathbb{R}^{3})\) and that the energy of Pauli-Villars may be extended in a unique way as a continuous application defined on \(\overset{.}{H}^{1}( \mathbb{R}^{3})\times \overset{.}{H}_{\mathrm{div}}^{1}(\mathbb{R}^{3})\), under appropriate hypotheses on the coefficients and masses of the Pauli-Villars energy. They also quote from this paper the result proving that the electromagnetic potential which is the solution in \(\overset{.}{H} ^{1}(\mathbb{R}^{3})\times \overset{.}{H}_{\mathrm{div}}^{1}(\mathbb{R}^{3})\) of two nonlinear Poisson equations is also the solution of a min-max problem, both problems involving a charge density and a current density which satisfy uniform estimates and other properties. The authors then quote from the HAL-preprint hal-01270637v2, written by three of them, the derivation of the Euler-Heisenberg model from that of Pauli-Villars. They end with the presentation of a renormalization process applied to the Euler-Heisenberg model.
scientific article; zbMATH DE number 6692664
scientific article