QCD as a Quantum Link Model

TL;DR

This paper presents a novel quantum link model formulation of QCD using non-commuting operators in a higher-dimensional lattice, incorporating quarks naturally and offering promising analytic and computational advantages.

Contribution

It introduces a quantum link model for QCD with a fifth Euclidean dimension and a rishon fermionic representation, enabling new analytic and computational approaches.

Findings

Formulates QCD as a quantum link model with a fifth Euclidean dimension.

Incorporates quarks via Kaplan's fermion method without fine-tuning.

Expresses the Hamiltonian in terms of glueball, meson, and quark operators.

Abstract

QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCD is formulated with a fifth Euclidean dimension, whose extent resembles the inverse gauge coupling of the resulting four-dimensional theory after dimensional reduction. The inclusion of quarks is natural in Shamir's variant of Kaplan's fermion method, which does not require fine-tuning to approach the chiral limit. A rishon representation in terms of fermionic constituents of the gluons is derived and the quantum link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of glueball, meson and constituent quark operators. The new formulation of QCD is promising both from an analytic and from a computational point of view.