Poisson Algebra of Wilson Loops and Derivations of Free Algebras

Details Poisson Algebra of Wilson Loops and Derivations of Free Algebras Poisson Algebra of Wilson Loops and Derivations of Free Algebras

1995-08-22

arxiv.org/abs/hep-th/9508103v1

J.Math.Phys. 37 (1996) 637-649

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, no special macros necessary

Scientific paper

10.1063/1.531433

We describe a finite analogue of the Poisson algebra of Wilson loops in Yang-Mills theory. It is shown that this algebra arises in an apparently completely different context; as a Lie algebra of vector fields on a non-commutative space. This suggests that non-commutative geometry plays a fundamental role in the manifestly gauge invariant formulation of Yang-Mills theory. We also construct the deformation of the loop algebra induced by quantization, in the large N_c limit.

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