Regularization dependence of the zero mode dynamics in the Schwinger model

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 L → ∞ the gauge field can be localized or delocalized depending on the regulator.