Problem of Proving the Mandelstam Representation

Abstract

It is shown that sufficiency conditions for the validity of the Mandelstam representation of a collision amplitude can be stated in terms of the location of singularities of its physical branch when one of the energy variables is real and positive and the second independent energy variable is complex. It is also shown that in perturbation theory the real singularities of the physical branch must correspond to positive Feynman parameters provided that none of the curves of singularities identified in this way have turning points in positive spectral regions. The same condition will exclude complex singularities in the physical sheet that are connected to the curves of singularities on its real boundary. If there are any disconnected complex singularities they must correspond to complex Feynman parameters.