Fermion mass and width in QED in a magnetic field

TL;DR

This paper analyzes how a strong magnetic field affects the fermion mass and width in QED, revealing that the mass acquires an imaginary part due to Landau level contributions, which diminishes at very high field strengths.

Contribution

It provides a detailed calculation of the fermion self-energy in a magnetic field, including sub-leading Landau level effects, and describes the resulting mass spectral density and stability.

Findings

Mass develops an imaginary part due to Landau levels beyond the lowest one.

The spectral density indicates a finite probability for fermions to occupy higher Landau levels.

At very high magnetic fields, the fermion becomes a stable particle in the lowest Landau level.

Abstract

We revisit the calculation of the fermion self-energy in QED in the presence of a magnetic field. We show that, after carrying out the renormalization procedure and identifying the most general perturbative tensor structure for the modified fermion {mass operator} in the large field limit, the mass develops an imaginary part. This happens when account is made of the sub-leading contributions associated to Landau levels other than the lowest one. The imaginary part is associated to a spectral density describing the spread of the mass function in momentum. The center of the distribution corresponds to the magnetic-field modified mass. The width becomes small as the field intensity increases in such a way that for asymptotically large values of the field, when the separation between Landau levels becomes also large, the mass function describes a stable particle occupying only the lowest Landau level. For large but finite values of the magnetic field, the spectral density represents a finite probability for the fermion to occupy Landau levels other than the LLL.