A Non-perturbative Estimate of Vacuum Polarization in QED

TL;DR

This paper provides a non-perturbative estimate of vacuum polarization effects in QED, offering a new approach to calculating the running coupling and beta function that differs significantly from traditional perturbative methods.

Contribution

It introduces a non-perturbative, convergent series expression for the one-loop effective action in QED to estimate the fine structure constant and beta function at any scale.

Findings

Non-perturbative estimate of the running coupling in QED

Demonstration of renormalization group invariance of the effective action

Significant contrast with perturbative results

Abstract

We present a new estimate of the fine structure constant and the $\beta$-function of QED at an arbitrary scale. Using the non-perturbative but convergent series expression of the one loop effective action of QED that has been available recently we make a non-perturbative estimate of the running coupling and the $\beta$-function, and prove the renormalization group invariance of the effective action. The contrast between our result and the perturbative result is remarkable.