# Lattice Fermions and Chiral Symmetry

## TL;DR

This paper introduces a new lattice fermion formulation that preserves chiral symmetry and avoids fermion doubling, requiring only a bare mass term to break chiral symmetry and recover the axial anomaly.

## Contribution

It presents a hermitian, chirally symmetric lattice fermion formulation using one-sided differences, eliminating fermion doubling and clarifying the role of the mass term in chiral symmetry breaking.

## Key findings

- Achieves fermion doubling elimination
- Maintains chiral symmetry except for a bare mass term
- Reproduces the axial anomaly in perturbation theory

## Abstract

We propose a formulation of lattice fermions with one-sided differences that is hermitian, chirally symmetric (barring a bare mass term) and completely free of doubling. To obtain the axial anomaly in perturbation theory it was necessary to break chiral symmetry on the lattice only through a bare mass term for the physical fermion. The chiral limit may be taken once the continuum limit is reached. We comment on the role of the mass term with examples elsewhere in field theory.