Integral Representations for Scattering Amplitudes in Perturbation Theory

Abstract

Some integral representations for scattering amplitudes are proposed, which are more general than the Mandelstam representation. Their support properties are investigated for some practical cases and for the general case in every order of perturbation theory. In the Appendices Nambu-Symanzik's formula is proved in terms of the Feynman parametric integral, and an example (for the two-particle scattering) is given in which stability conditions are satisfied but no dispersion relation holds.