A Generalized ``Surfaceless'' Stokes' Theorem

TL;DR

This paper introduces a generalized Stokes' theorem applicable in any dimension and for complex loops, eliminating the need for an auxiliary surface and revealing a higher rank gauge symmetry.

Contribution

It presents a new formulation of Stokes' theorem that works for arbitrary, possibly knotted or self-intersecting loops without auxiliary surfaces, and uncovers a higher rank gauge symmetry.

Findings

Valid in any dimension and for arbitrary loops

Does not require an auxiliary surface

Reveals a higher rank gauge symmetry

Abstract

We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the invariance under deformations of the surface used in the conventional formulation.