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A new local gauge invariant method is introduced in order to maximallysimplify the expression for a SU(2) non-Abelian field strength. The new tetradsintroduced in previous works are going to play a fundamental role in thealgorithm presented in this manuscript. Three new local gauge invariant objectsare going to guide us through the process of making a field strength blockdiagonal. The process is also covariant. Any non-trivial isospace fieldstrength projection will become block diagonal through this algorithm. Alongwith the local gauge invariant method already developed in order to diagonalizethe stress-energy tensor, we have with this new local gauge invariant method tomaximally simplify the field strength, a new gauge invariant method to classifyYang-Mills field theories.

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