$SU_q(2)$ Lattice Gauge Theory

TL;DR

This paper introduces a reformulation of lattice gauge theories using quantum groups, providing a two-parameter regularization framework that interpolates between known theories and approaches QCD in the continuum limit.

Contribution

It presents a novel Hamiltonian formulation where gauge symmetry is described by quantum groups, extending traditional lattice gauge theories with a deformation parameter.

Findings

Recovers Kogut-Susskind model at zero deformation parameter

Approaches continuum QCD as lattice spacing goes to zero for any deformation parameter

Proposes a two-parameter regularization scheme for QCD

Abstract

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters - the deformation parameter $\lambda$ and the lattice spacing $a$. We show that the system of Kogut and Susskind is recovered when $\lambda \rightarrow 0$, while QCD is recovered in the continuum limit (for any $\lambda$). We thus have the possibility of having a two parameter regularization of QCD.