Poisson brackets of normal-ordered Wilson loops

We formulate Yang-Mills theory in terms of the large-N limit, viewed as a c lassical limit, of gauge-invariant dynamical variables, which are closely r elated to Wilson loops, via deformation quantization. We obtain a Poisson a lgebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of (h) over bar operators. Comparing with a Poisson alg ebra one of us introduced in the past for Weyl-ordered quantum operators, w e find, using ideas closely related to topological graph theory, that these two Poisson algebras are, roughly speaking, the same. More precisely speak ing, there exists an invertible Poisson morphism between them. (C) 1999 Ame rican Institute of Physics. [S0022-2488(99)02204-5].