Asymptotic behavior of Wilson loops from Schroedinger equation on the gauge group

Details Asymptotic behavior of Wilson loops from Schroedinger equation on the gauge group Asymptotic behavior of Wilson loops from Schroedinger equation on the gauge group

2006-02-15

arxiv.org/abs/hep-th/0602154v1

Phys.Lett.B634:262-266,2006

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

10.1016/j.physletb.2006.02.001

Probability distribution of non-Abelian parallel transporters on the group manifold and the corresponding amplitude are investigated for quantum Yang-Mills fields. It is shown that when the Wilson area law and the Casimir scaling hold for the quantum gauge field, this amplitude can be obtained as the solution of the free Schroedinger equation on the gauge group. Solution of this equation is written in terms of the path integral and the corresponding action term is interpreted geometrically. We also note that the partition function of two-dimensional pure Yang-Mills theory living on the surface spanned on the loop solves the obtained equation.

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