A new fermion Hamiltonian for lattice gauge theory

TL;DR

This paper introduces a novel fermion Hamiltonian for lattice gauge theory using the overlap formula, exploring chiral charge properties and their implications for chiral anomalies.

Contribution

It formulates a new Hamiltonian approach for lattice gauge theory incorporating the overlap fermion method and analyzes chiral charge relations.

Findings

Chiral charge $Q_5$ commutes with the fermionic Hamiltonian $H_f$

Relation between chiral charge and fermion energy impacts chiral anomaly understanding

New formulation offers insights into lattice gauge theory Hamiltonians

Abstract

We formulate Hamiltonian vector-like lattice gauge theory using the overlap formula for the spatial fermionic part, $H_f$. We define a chiral charge, $Q_5$ which commutes with $H_f$, but not with the electric field term. There is an interesting relation between the chiral charge and the fermion energy with consequences for chiral anomalies.