Thompson's Method applied to Quantum Electrodynamics (QED)

TL;DR

This paper applies Thompson's method to QED to derive the energy scale dependence of the coupling constant and mass, offering an alternative to traditional renormalization group techniques with simplified calculations at the critical dimension.

Contribution

It introduces Thompson's method as a straightforward alternative to the renormalization group for analyzing QED's scale dependence of coupling and mass.

Findings

Derived the running of the coupling constant ppa() with energy scale.

Obtained the logarithmic dependence of mass on energy scale.

Validated the method at the critical dimension d_c=4.

Abstract

In this work we apply Thompson's method (of the dimensions) to study the quantum electrodynamics (QED). This method can be considered as a simple and alternative way to the renormalisation group (R.G) approach and when applied to QED lagrangian is able to obtain the running coupling constant behavior $\alpha (\mu)$, namely the dependence of $\alpha$ on the energy scale. We also obtain the dependence of the mass on the energy scale. The calculations are evaluated just at $d_c=4$, where $d_c$ is the upper critical dimension of the problem, so that we obtain logarithmic behavior both for the coupling $\alpha$ and the mass $m$ on the energy scale $\mu$.