Connection between momentum cutoff and operator cutoff regularizations

Operator cutoff regularization based on the original Schwinger proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual momentum cutoff prescription yet preserves gauge symmetry even in the presence of the cutoff scales. The similarity between the operator cutoff regularization and the method of higher (covariant) derivatives is also observed. The invariant nature of the operator cutoff regularization makes it a promising tool for exploring the renormalization group how of gauge theories in the spirit of the Wilson-Kadanoff blocking transformation.