Mandelstam Representation for Potential Scattering

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Abstract
A proof of the Mandelstam representation for the nonrelativistic scattering amplitude is given when the potential is of the Yukawa form or (by obvious extension) a suitable linear combination of such forms. The analytic properties of the scattering amplitude as a function of momentum transfer are established by using only a finite sequence of equivalent definitions of the scattering amplitude. By studying the Born series for individual partial waves, it is shown in addition that there cannot be an essential singularity at infinity. Together, these results imply both dispersion relations for individual partial waves and the Mandelstam representation.