Abstract
In this paper, certain results concerning the singularities of holomorphic functions with integral representations are used to investigate the analytic properties of the elastic unitarity integral of the quantum theory of fields. In particular, it is shown that each of the Landau singularities of the scattering amplitude is an actual singularity. It is also shown that if the scattering amplitude is not identically zero it must have a natural boundary on the unphysical sheet.
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