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 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 algorithm. Along with the local gauge invariant method already developed in order to diagonalize the stress-energy tensor, we have with this new local gauge invariant method to maximally simplify the field strength, a new gauge invariant method to classify Yang-Mills field theories.