Previous work on phase contours is extended to include reaction amplitudes that have Regge behavior at high energies. General results are obtained on relations between resonance poles and surfaces of zeros of the collision amplitudes. These results depend on the symmetry properties of the amplitudes and on the nature of the dominant Regge trajectories and the dominant resonances. They are also affected by the spin of the colliding particles. Zeros of collision amplitudes can be located asymptotically from Regge formulas, and along certain symmetry lines they can be located at finite values of the energy variables by means of a narrow-resonance approximation. We relate the asymptotic zeros and these "symmetry" zeros by making a unitarity hypothesis. This leads to bootstrap conditions which are generalizations of the linear constraints contained in the Veneziano model.

• Received 17 December 1968

DOI:https://doi.org/10.1103/PhysRev.182.1669