PHYSICAL-REGION DISCONTINUITY EQUATIONS FOR MANY-PARTICLE SCATTERING AMPLITUDES .I.

The discontinuity equations are derived for all singularities of multiparticle scattering functions that enter the portion of the physical region lying below the four-particle threshold. These equations, which are the precise statements of the Cutkosky formulas, are calculated directly from the unitarity equations. The only analyticity properties used are those obtained from the S-matrix macroscopic-causality condition. That is, the scattering functions are taken to be analytic in the physical region except on positive-α Landau surfaces, around which they continue in accordance with the well-defined plus-i∈ rule. Copyright © 1969 by the American Institute of Physics.