Through a series of papers many results in group theory have been proven. These results establish a direct link between the local gauge groups of transformations of the Standard Model and local groups of transformations of a new kind of tetrad vectors in four-dimensional Lorentzian spacetimes. These links between these two sets of local groups of transformations are isomorphisms. Because the local planes of covariant diagonalization of stress-energy tensors in Yang-Mills theories have been proven to be the local planes of gauge symmetry, simultaneously. It is in this context that we wish to establish a new kind of relationship. We will explore the possible application of local tetrad transformations in order to turn a non-null tetrad into a null tetrad. We will explore this possibility using pure Riemannian geometry. We can describe the local transformation of non-null fields into null fields through local internal transformations with associated four-dimensional Lorentzian spacetimes. It is not possible to transform timelike or spacelike vectors into null vectors through coordinate transformations. We will achieve this goal through local electromagnetic gauge transformations or even local Yang-Mills non-Abelian gauge transformations. We will discuss this application in microparticle process of annihilation, rare decays and the Drell-Yan process.
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