Analyticity and Unitarity of Relativistic Off-Shell Models

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Abstract
In this paper we discuss two questions concerning off-shell relativistic models not involving integration over relative energy: (i) Is it possible to obtain a unitary off-shell model with simple potential whose singularity structure is a reasonable approximation to that of Mandelstam? (ii) Is it possible to derive an off-shell model satisfying two- and three-body unitarity by a consistent procedure from a basic field-theory model? On the first point we analyze the singularity structure of three proposed models satisfying two-particle unitarity and show that their singularity structures deviate as much from the Mandelstam form as that of the Blankenbecler-Sugar equation. On the second point we generalize one of these two-particle models to incorporate three-particle unitarity, deriving the generalization from an analysis of the ladder-approximated dressed-rung Bethe-Salpeter equation.

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