$S{U}_q(2)$ Lattice Gauge Theory

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 $\lambda \to 0$, while QCD is recovered in the continuum limit (for any $\lambda$). We thus have the possibility of having a two parameter regularization of QCD.

26 pages, LATEX file

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• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Bicovariant Calculus in Quantum Theory and a Generalization of the Gauss Law
• Deformed Chern-Simons Theories
• Hidden Quantum Group Symmetry in the Chiral Model