Using the coherent-state representation we write down a set of relations that must be satisfied by scattering amplitudes having full $s$-channel and elastic $t$-channel unitarity. While general solutions to this set of equations have not been found, we discuss several models that illustrate certain aspects of the problem. In particular we show that the "Born term" in the $t$-channel equation must itself satisfy full $s$-channel unitarity. Some properties of functional integration are discussed.

• Received 19 August 1974

DOI:https://doi.org/10.1103/PhysRevD.11.1673