A Gauge-Invariant Regularization of the Weyl Determinant Using Wavelets

Abstract

In line with a previous paper, a gauge-invariant regularization is developed for the Weyl determinant of a Euclidean gauged chiral fermion. We restrict ourselves to gauge configurations with the $A$ field going to zero at infinity in Euclidean space; and thus restrict gauge transformations to those with $U$ the identity at infinity. For each finite cutoff one gets a strictly gauge-invariant expression for the Weyl determinant. Full Euclidean invariance is only to be sought in the limit of removing the cutoff. We expect the limit to be Euclidean invariant, but this has not yet been proved. One need not enforce the no-anomaly condition on the representation of the gauge group! We leave to future research relating the present results to conventional physics wisdom.