Fractional and Integer Charges from Levinson's Theorem

TL;DR

This paper uses phase shifts and Levinson's theorem to compute fermion quantum numbers in background fields, extending scattering theory to higher dimensions and applying dimensional regularization to eliminate anomalies.

Contribution

It introduces a method to compute fermion charges using phase shifts and Levinson's theorem, extending to arbitrary dimensions with dimensional regularization.

Findings

Regularization removes vector current anomalies.

Method applicable to bag models in 1D and 3D.

Demonstrates consistency of fermion charge calculations.

Abstract

We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1+1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions.