Two effective models for the Dirac vacuum in electromagnetic fields
type: Item
instance of: scholarly article
title: Two effective models for the Dirac vacuum in electromagnetic fields
zbMATH Open document ID: 1362.35247
author: Philippe Gravejat
author: C. Hainzl
author: M. Lewin
author: Éric Séré
published in: Séminaire Laurent Schwartz. EDP et Applications
publication date: 2017-03-07T00:00:00Z
review text: 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.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81V10
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 6692664
zbMATH Keywords: Dirac void
zbMATH Keywords: electromagnetic field
zbMATH Keywords: Pauli-Villars model
zbMATH Keywords: Euler-Heisenberg model
zbMATH Keywords: nonlinear Poisson equation
zbMATH Keywords: min-max problem
zbMATH Keywords: renormalization
MaRDI profile type: Publication
full work available at URL: slsedp.89
OpenAlex ID: W2501940691
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DOI: 10.5802/SLSEDP.89
description: scientific article; zbMATH DE number 6692664