Selfconsistent solution for the polarized vacuum in a nophoton QED model
Abstract
We study the BogoliubovDiracFock model introduced by Chaix and Iracane (1989 J. Phys. B: At. Mol. Opt. Phys. 22 3791814) which is a meanfield theory deduced from nophoton QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a selfconsistent equation. In a recent paper, we proved the convergence of the iterative fixedpoint scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cutoff Λ and the bare fine structure constant α. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cutoff Λ and without any constraint on the external field. We also study the behaviour of the minimizer as Λ goes to infinity and show that the theory is 'nullified' in that limit, as predicted first by Landau: the vacuum totally cancels the external potential. Therefore, the limit case of an infinite cutoff makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant α, on a simplified model where the exchange term is neglected.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2005
 DOI:
 10.1088/03054470/38/20/014
 arXiv:
 arXiv:physics/0404047
 Bibcode:
 2005JPhA...38.4483H
 Keywords:

 Physics  Atomic Physics;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 Final version, to appear in J. Phys. A: Math. Gen