Renormalization of Dirac's Polarized Vacuum

TL;DR

This paper reviews a mean-field model for relativistic electrons that captures the self-consistent behavior of the polarized Dirac sea, derived from QED, and discusses charge renormalization as the ultraviolet cutoff is removed.

Contribution

It introduces a mean-field model for relativistic electrons in atoms and molecules that includes the polarized Dirac sea and analyzes the charge renormalization process.

Findings

Existence of solutions with an ultraviolet cutoff.

Analysis of the limit as the cutoff goes to infinity.

Implementation of charge renormalization in the model.

Abstract

We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\Lambda$. We then discuss the limit $\Lambda\to\infty$ in detail, by resorting to charge renormalization.