Gauge invariant method for maximum simplification of the field strength in non-Abelian Yang-Mills theories

TL;DR

This paper introduces a novel gauge invariant method to simplify the non-Abelian SU(2) field strength, enabling block diagonalization and the discovery of new local observables in Yang-Mills theories.

Contribution

A new gauge invariant algorithm utilizing tetrads and three invariant objects to simplify and block diagonalize non-Abelian field strengths.

Findings

Successfully block diagonalizes non-Abelian field strengths

Identifies new local gauge invariant observables

Maintains covariance throughout the process

Abstract

A new local gauge invariant method is introduced in order to maximally simplify the expression for a SU(2) non-Abelian field strength. The new tetrads introduced in previous works are going to play a fundamental role in the algorithm presented in this manuscript. Three new local gauge invariant objects are going to guide us through the process of making a field strength block diagonal. The process is also covariant. Any non-trivial isospace field strength projection will become block diagonal through this gauge invariant algorithm. As an application we will find new local observables in Yang-Mills theories.