Non-Abelian Stokes Theorem and Computation of Wilson Loop

TL;DR

The paper discusses how applying the non-Abelian Stokes theorem to Wilson loop operators can lead to ambiguities in non-trivial gauge fields, highlighting issues in non-local operator computations.

Contribution

It reveals the ambiguity problem in using the non-Abelian Stokes theorem for Wilson loops in non-trivial gauge fields, with illustrative examples.

Findings

Ambiguity arises in Wilson loop computations with non-trivial gauge fields.

Non-Abelian Stokes theorem may not be straightforwardly applicable in all cases.

Illustrative examples demonstrate the ambiguity in specific non-local operators.

Abstract

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.