Regularization dependence on the Schwinger-Dyson equation in Abelian gauge theory: 4D vs 3D cutoff regularization

TL;DR

This paper investigates how different cutoff regularizations (4D and 3D) affect solutions to the quenched Schwinger-Dyson equations in Abelian gauge theory, finding minimal impact and supporting their interchangeable use.

Contribution

It compares 4D and 3D cutoff regularizations in Schwinger-Dyson equations, demonstrating their similar effects in Abelian gauge theory.

Findings

Solutions are not drastically affected by the choice of regularization.

Both regularizations can be used effectively in analyses.

Regularization choice has minimal impact on results.

Abstract

We study the regularization dependence on the quenched Schwinger-Dyson equations in general gauge by applying the two types of regularizations, the four and three dimensional momentum cutoffs. The obtained results indicate that the solutions are not drastically affected by the choice of two different cutoff prescriptions. We then think that both the regularizations can nicely be adopted in the analyses for the Schwinger-Dyson equations.