Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory

Details Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory

1994-10-07

arxiv.org/abs/hep-th/9410053v1

Int. J. Mod. Phys. A10 (1995) 2479

Physics

High Energy Physics

High Energy Physics - Theory

32 Pages, 7 figures upon request

Scientific paper

We formulate the canonical structure of Yang--Mills theory in terms of Poisson brackets of gauge invariant observables analogous to Wilson loops. This algebra is non--trivial and tractable in a light--cone formulation. For U(N) gauge theories the result is a Lie algebra while for SU(N) gauge theories it is a quadratic algebra. We also study the identities satsfied by the gauge invariant observables. We suggest that the phase space of a Yang--Mills theory is a co--adjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

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