Longitudinal Rescaling of Quantum Electrodynamics

TL;DR

This paper studies how quantum electrodynamics behaves under longitudinal rescaling using Wilsonian renormalization, revealing anomalous scaling behaviors of couplings at one-loop order.

Contribution

It applies aspherical Wilsonian renormalization to quantum electrodynamics to analyze its behavior under longitudinal rescaling at one-loop order, extending methods used in Yang-Mills theory.

Findings

Identifies anomalous powers of the rescaling parameter in renormalized couplings.

Demonstrates the validity of perturbation theory only for mbda sim 1.

Provides insights into the scaling behavior of QED at high energies.

Abstract

We investigate quantum longitudinal rescaling of electrodynamics, transforming coordinates as $x^{0,3}\to\lambda x^{0,3}$ and $x^{1,2}\to x^{1,2}$, to one loop. We do this by an aspherical Wilsonian renormalization, which was applied earlier to pure Yang-Mills theory. We find the anomalous powers of $\lambda$ in the renormalized couplings. Our result is only valid for $\lambda \lesssim 1$, because perturbation theory breaks down for $\lambda \ll 1$.