Simple ansatz for the lattice fermion determinant

TL;DR

The paper proposes a non-local lattice fermion ansatz that accurately reproduces continuum limits, chiral anomalies, and maintains gauge invariance, addressing issues with non-smooth gauge fields.

Contribution

It introduces a novel ansatz for the lattice fermion determinant that preserves key continuum properties and gauge invariance.

Findings

Reproduces correct continuum limit for finite order diagrams

Ensures consistent chiral anomalies on the lattice

Maintains gauge invariance of the fermion functional

Abstract

An ansatz for the fermion vacuum functional on a lattice is proposed. It is proved to reproduce correct continuum limit for convergent diagrams of any finite order in smooth external fields, as well as consistent chiral anomalies, and ensures gauge invariance of the absolute value of the functional at any lattice spacing. The ansatz corresponds to a certain non-local fermion action having global chiral invariance. Problems caused by non-smooth gauge fields are discussed.