Non-Abelian Stokes Theorem for Loop Variables Associated with Nontrivial Loops

TL;DR

This paper derives a non-Abelian Stokes theorem applicable to complex loops like knots and links, revealing that loop variables can differ from unity even with zero field strength on the enclosed surface.

Contribution

It introduces a generalized non-Abelian Stokes theorem for nontrivial loops, extending previous formulations to include knots and links.

Findings

Loop variables differ from unity despite zero field strength on the surface

The theorem applies to nontrivial loops such as knots and links

Provides insight into gauge theories with complex loop structures

Abstract

The non-Abelian Stokes theorem for loop variables associated with nontrivial loops (knots and links) is derived. It is shown that a loop variable is in general different from unity even if the field strength vanishes everywhere on the surface surrounded by the loop.