By assuming analyticity in the energy, plane and using unitarily, it is found that the relativistic scattering amplitudes of general processes have no singularities in the energy plane except branch points at the thresholds, when keeping the momentum transfer variables in their physical range. These branch points are of the square root type or logarithmic according to whether the number of particles in the corresponding intermediate states is even or odd respectively, The normal threshold behaviour of the Feynman amplitudes is considered in detail and is found to agree with the above results.
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