On the Analytic Structure of Production Amplitudes

The analytic structure of two-particle to three-particle production amplitudes is examined within the framework of analytic $S$-matrix theory, with particular emphasis on the structure of the physical sheet. The basic principle used is maximal analyticity, which is both discussed and exemplified. The knowledge of the structure of the physical sheet is used in deriving formulas for the discontinuities across the cuts in the two-particle subenergies of the three-particle channel and across the cut in the total energy.