QCD as a quantum link model

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.

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

“…In section 2, we begin with the simpler case of Abelian gauge theories. In order to address nonperturbative effects, we regularize the theory on a lattice, first following the classical Wilson formulation [51], and then extending the concept of lattice gauge theories to quantum link models [76][77][78][79]. The resulting Abelian gauge theories resemble models of condensed matter physics and quantum information theory.…”

Towards quantum simulating QCD

“…The first U(1) and S U(2) gauge theories formulated with (generalized) quantum spins were constructed by Horn [49], and further investigated by Orland and Rohrlich under the name of gauge magnets [50]. Quantum link models [51,52,53] provide an alternative to Wilson's lattice gauge theory [54,55,56] for defining QCD beyond perturbation theory. Both in the Wilson formulation and in quantum link models, the basic gauge degrees of freedom are associated with the links connecting nearest-neighbor sites of a lattice that serves as a regulator of ultra-violet divergences.…”

Quantum link models with many rishon flavors and with many colors

“…In order to study full QCD, fermions should be included. By pairing rishon and quark operators, the theory can be completely bosonized [5] which would be a significant advantage in numerical simulations.…”

“…thus breaking the unwanted U (1) [5]. The SU (2N c ) generators may be expressed as products of fermionic creation and annihilation operators, which obey canonical anticommutation relations: For these representations the determinant term in (4) is non-trivial and hence the unwanted U (1) symmetry is broken.…”