Complex Negative-Signature Trajectories and the Pomeranchuk Theorem

Within the framework of complex-angular-momentum methods, it is shown that amplitudes which violate the Pomeranchuk theorem require negative-signature trajectories which are of the form α(t)=1±const√t+O(t) near $t=0$. There must be corresponding positive-signature trajectories. The character of the singular surfaces with negative signature is discussed briefly.