Lattice fermions with gauge noninvariant measure

TL;DR

This paper introduces a lattice formulation of Weyl fermions with a gauge noninvariant measure, demonstrating that one variant restores gauge invariance in the continuum limit and discussing a potential perfect regularization.

Contribution

It presents a novel lattice approach for Weyl fermions with a gauge noninvariant measure and shows how gauge invariance can be restored in the continuum limit.

Findings

One variant restores gauge invariance in the continuum limit.

Perturbative calculations confirm the gauge invariance restoration.

Discussion of a 'perfect' regularization method for chiral fermions.

Abstract

We define Weyl fermions on a finite lattice in such a way that in the path integral the action is gauge invariant but the functional measure is not. Two variants of such a formulation are tested in perturbative calculation of the fermion determinant in chiral Schwinger model. We find that one of these variants ensures restoring the gauge invariance of the nonanomalous part of the determinant in the continuum limit. A `perfect' perturbative regularization of the chiral fermions is briefly discussed.