$SU_q(2)$ Lattice Gauge Theory

Details $SU_q(2)$ Lattice Gauge Theory $SU_q(2)$ Lattice Gauge Theory

1996-02-17

arxiv.org/abs/hep-th/9602094v1

Phys.Rev. D54 (1996) 1054-1062

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LATEX file

Scientific paper

10.1103/PhysRevD.54.1054

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.

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