Vacuum polarization correction to atomic energy levels in the path integral formalism

TL;DR

This paper develops a path integral approach to calculate vacuum polarization effects on atomic energy levels, incorporating strong nuclear fields and providing numerical predictions for experimental tests of quantum electrodynamics.

Contribution

It introduces a perturbative path integral formalism that treats strong nuclear fields to all orders and derives expressions for vacuum polarization energy shifts.

Findings

Derived formulas for vacuum polarization energy shifts.

Numerical estimates for potential experimental tests.

Framework applicable to strong-field quantum electrodynamics.

Abstract

Vacuum polarization corrections to the energy levels of bound electrons are calculated using a perturbative path integral formalism. We apply quantum electrodynamics in a framework which treats the strong binding nuclear field to all orders. The effective potential, derived from the Dyson-Schwinger equation for the photon propagator, is then considered pertubatively. Expressions for the vacuum polarization shift of binding energies is obtained from the poles of the spectral function up to second order. Numerical results are provided to select candidates for novel tests of strong-field quantum electrodynamics by means of precision mass spectrometry.