Lattice representation of vector and chiral gauge theories

TL;DR

This paper introduces a lattice derivative using Fourier transforms, addresses species doubling with boundary conditions, modifies chiral transformations to reproduce anomalies, and constructs chiral gauge theories with Weyl fermions.

Contribution

It presents a novel lattice derivative definition and a method to construct chiral gauge theories with a single Weyl fermion, addressing key issues in lattice gauge theory.

Findings

Successfully removes species doublers with anti-periodic boundary conditions.

Reproduces chiral anomaly through modified chiral transformation.

Enables construction of chiral gauge theories on the lattice.

Abstract

A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral gauge theories can be constructed on the lattice using a single Weyl fermion as a building block.