Non-Abelian Stokes Theorem and Computation of Wilson Loop
نویسندگان
چکیده
It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is illustrated by the specific examples of the computation of a non-local operator. The non-Abelian Stokes theorem is widely applied to compute Wilson loop (closed nonAbelian phase factor), Ψ(C) = Pexp (ig ∮ C dz Aμ(z)) (Aμ is the simplified notation for dimG ∑ a=1 AμT ), which is important for the construction of gauge invariant operators in the nonperturbative approaches to QCD. The power of the theorem lies in transforming the line integral in a Wilson loop to a more tractable surface integral over the surface S enclosed by contour C: Pexp (
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