Chiral Symmetry Breaking and Point-Splitting Procedure in Light-Cone Quantized QED in a Magnetic Field

TL;DR

This paper investigates how point-splitting regularization can prevent light-cone singularities in the calculation of dynamical electron mass in QED under strong magnetic fields, ensuring consistent results in light-cone quantization.

Contribution

It demonstrates the effectiveness of point-splitting regularization in avoiding singularities in light-cone QED calculations with magnetic fields and discusses integrating this method into the theory's Lagrangian.

Findings

Point-splitting regularization prevents light-cone singularities.

Dynamical electron mass can be consistently calculated in strong magnetic fields.

Implementation of regularization into the Lagrangian is feasible.

Abstract

The summation of all rainbow diagrams in QED in a strong magnetic field leads to a dynamical electron mass on the light-cone. Further contributions to this summation however can cause problems with light-cone singularities. It is shown that these problems are generally avoided by applying the point-splitting regularization to every diagram. The possibility of implementing this procedure into the Lagrangian of the theory is discussed.