Poisson Brackets of Normal-Ordered Wilson Loops

Details Poisson Brackets of Normal-Ordered Wilson Loops Poisson Brackets of Normal-Ordered Wilson Loops

1998-10-28

arxiv.org/abs/hep-th/9810233v3

J.Math.Phys. 40 (1999) 1870-1890

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 4 eps figures, LaTeX2.09; citations added

Scientific paper

We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of $\hbar$) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum operators, we find, using ideas closly related to topological graph theory, that these two Poisson algebras are, roughly speaking, the same. More precisely speaking, there exists an invertible Poisson morphism between them.

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