Unitarity and Production Amplitudes

Abstract

A development of the $\frac{N}{D}$ formulation of the unitary $S$ matrix is presented for multichannel reactions including production processes. The relevant amplitudes are expressed in terms of helicity amplitudes and the coupled, unitarity relations of Blankenbecler. The analytic continuation of the amplitudes in the presence of anomalous thresholds is considered in detail. An extension of the Levinson theorem to the multichannel production case is discussed. An application of the formalism developed here is given in another paper.