It is shown for the third-order triangle and the fourth-order box Feynman diagrams that singularities exist on the physical boundaries of the amplitudes if, and only if, the external momenta are such as to allow the reactions to actually proceed with real intermediate particles. If, furthermore, the information concerning the locations and appropriate branches of singularities implied by this principle is combined with the requirement that discontinuities be given by Cutkosky's rules, the amplitudes are uniquely determined.

• Received 23 April 1964

DOI:https://doi.org/10.1103/PhysRev.135.B1381