Chiral fermion in the Hamiltonian lattice gauge theory

TL;DR

This paper explores the implementation of chiral fermions in Hamiltonian lattice gauge theory, demonstrating how to define compatible operators, analyze spectral properties, and relate different fermion formulations to chiral phenomena.

Contribution

It introduces a method to define a commuting chiral charge operator for overlap fermions and analyzes spectral signatures of chiral properties in lattice systems.

Findings

Eigenvalues of energy and chiral charge can be simultaneously defined.

Wilson fermion can be viewed as a chiral fermion in one dimension.

Spectral analysis reveals chiral characteristics like anomalies.

Abstract

We discuss the chiral fermion in the Hamiltonian formalism of lattice gauge theory. Although the naive chiral charge operator does not commute with the Hamiltonian, the commutable one can be defined for the overlap fermion. The eigenvalues of the energy and the chiral charge can be defined simultaneously. We study how the eigenvalue spectrum reflects chiral properties of systems, such as a chiral chemical potential and the axial anomaly. We also show that the Wilson fermion is a chiral fermion in one dimension.