On the Non-Abelian Stokes Theorem
Dmitri Diakonov, Victor Petrov (NORDITA, St.Petersburg NPI)
TL;DR
This paper clarifies the non-Abelian Stokes theorem for Wilson loops, addresses recent criticisms, and derives a lattice regularized variant, reinforcing its mathematical validity and applicability.
Contribution
The paper defends the non-Abelian Stokes theorem against recent mathematical criticisms and provides a lattice regularization version.
Findings
The theorem's validity is mathematically sound.
Criticisms were based on mathematical errors.
A lattice regularized formula for Wilson loops is derived.
Abstract
We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Fluid Dynamics and Turbulent Flows · Advanced Numerical Methods in Computational Mathematics