Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double

Details Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double

1995-01-31

arxiv.org/abs/hep-th/9501143v1

Mod.Phys.Lett. A10 (1995) 2619-2632

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, latex, no figures

Scientific paper

It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge $A_{0}=0$ one should place on every link the cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the paper that there is a generalization of the usual Hamiltonian formulation to the case of the Heisenberg double.

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