Regularization Dependence of the Zero Mode Dynamics in the Schwinger Model

TL;DR

This paper compares two regularization methods in the Schwinger model, showing how they differently influence the zero mode dynamics and gauge field localization, highlighting the importance of regularization choice.

Contribution

It demonstrates the dependence of zero mode dynamics on regularization schemes in the Hamiltonian formulation of the Schwinger model.

Findings

Heatkernel and sharp cutoff regularizations yield different effective potentials.

The difference in effective potential is independent of fermionic configurations.

Gauge field localization depends on the chosen regularization.

Abstract

I compare heatkernel regularization with sharp gauge invariant cutoffs in the Hamiltonian formulation of the Coulomb gauged Schwinger model on a circle. The effective potential for the zero mode of the gauge field in a given fermionic configuration is different in these two regularizations, the difference being independent of the chosen fermionic configuration. In the continuum limit the gauge field can be localized or delocalized depending on the regulator.