Vacuum polarization in Uranium

TL;DR

This paper develops a functional integral approach to the Hartree-Fock method, calculates vacuum polarization effects nonperturbatively for the Dirac-Coulomb operator, and applies the method to approximate uranium's vacuum polarization.

Contribution

It introduces a novel functional integral formulation of the Hartree-Fock method and computes nonperturbative vacuum polarization effects for heavy atoms like uranium.

Findings

Numerical calculation of vacuum polarization flow for Dirac-Coulomb operator

Rescaled flow integration for Hartree-Fock operator

Approximate vacuum polarization in Uranium

Abstract

We formulate the Hartree-Fock method using a functional integral approach. Then we consider a nonperturbative component of the vacuum polarization. For the Dirac-Coulomb operator the renormalization flow of the vacuum polarization is calculated numerically. For the Hartree-Fock operator the polarization is obtained by integrating an appropriately rescaled flow. The text includes an approximate calculation of the vacuum polarization in Uranium.