The role of shape operator in gauge theories

TL;DR

This paper introduces a shape operator concept in Yang-Mills theories, providing new gauge-invariant variables as an alternative to traditional gauge potentials, potentially offering new insights into gauge theories.

Contribution

It proposes a novel geometric approach using the shape operator and rotating blade to define gauge-invariant variables in Yang-Mills theories.

Findings

Introduction of shape operator as a gauge-invariant variable

Alternative to traditional gauge potentials in Yang-Mills theories

Potential new tools for analyzing gauge invariance

Abstract

We introduce the concept of shape operator and rotating blade (also known in the theory of embedded Riemannian manifolds as the second fundamental form and the Gauss map) in the realm of Yang-Mills theories. Hence we arrive at new gauge-invariant variables, which can serve as an alternative to the usual gauge potentials.