The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes
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By means of a kinematic analysis of tree level graviton amplitudes we find, at least through six points, that the reason of their decomposition as a sum over products of gauge boson amplitudes is on-shell gauge invariance and unitarity. As a by-product of our analysis we find nonlinear relations obeyed by Yang-Mills amplitudes. All our results are valid for arbitrary spacetime dimensions.