Results on the Analyticity of Many‐Body Scattering Amplitudes in Perturbation Theory

Abstract

The problem of analytic continuation of the many‐body scattering amplitude associated with a perturbation‐theory diagram under the rotation of the final momenta from real to complex momenta, k → (1 + iθ)k, is studied. It is shown that the contour of integration over internal momenta can be distorted avoiding singularities of the integrand, as θ varies for small enough θ. If the diagram is connected enough, the potentials are Yukawa‐type, Re E > 0, and Im E < 0. The rotation angle can be picked independently of Im E.