On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations

TL;DR

This paper explores an operator cutoff regularization method based on Schwinger's proper-time formalism, demonstrating its gauge invariance and similarity to higher derivative methods, with potential applications in gauge theory renormalization.

Contribution

It introduces a gauge-invariant operator cutoff regularization scheme that mimics momentum cutoffs and relates to higher derivative methods, useful for renormalization group studies.

Findings

Regularization preserves gauge symmetry with cutoff scales.

Operator cutoff mimics momentum cutoff behavior.

Potential for studying gauge theory renormalization flows.

Abstract

Operator cutoff regularization based on the original Schwinger's 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. 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 flow of gauge theories in the spirit of Wilson-Kadanoff blocking transformation.