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

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 paper. 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 nontrivial 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.