  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.
