Numerical Investigation of Fermion Mass Generation in QED

TL;DR

This paper non-perturbatively investigates fermion mass generation in QED using Schwinger-Dyson equations, analyzing quenched and unquenched cases with advanced numerical methods to ensure accuracy and proper divergence handling.

Contribution

It develops a numerical approach to solve coupled Schwinger-Dyson equations in full QED, including unquenched effects, with careful divergence cancellation and solution smoothness considerations.

Findings

Identified critical coupling for mass generation in quenched QED.

Developed a high-accuracy numerical method for unquenched QED equations.

Ensured proper cancellation of quadratic divergences in vacuum polarization.

Abstract

We investigate the dynamical generation of fermion mass in quantum electrodynamics (QED). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and the photon propagator. First, we study dynamical fermion mass generation in quenched QED with the Curtis-Pennington vertex, which satisfies the Ward-Takahashi identity and ensures the multiplicative renormalizability of the fermion propagator. We apply bifurcation analysis to determine the critical point for a general covariant gauge. In the second part of this work we investigate the dynamical generation of fermion mass in full, unquenched QED. We develop a numerical method to solve the system of three coupled non-linear equations for the dynamical fermion mass, the fermion wavefunction renormalization and the photon renormalization function. Much care is taken to ensure the high accuracy of the solutions. We also discuss in detail the proper numerical cancellation of the quadratic divergence in the vacuum polarization integral and the need to use smooth approximations to the solutions.