Abstract
In this, the first of two papers treating pion-nucleon collision and single-pion production, we study the requirements of unitarity and describe its effects on the analytic structure of the production amplitude. We do this by first carefully defining the physical amplitudes in the three-body helicity formalism. These amplitudes are then substituted into the unitarity equation and this unitarity equation is separated into a system of discontinuity equations. We also study the effects of possible driving terms. All this formalism is used to formulate a model of the production process. This model will be defined and solved in a subsequent paper.
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