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

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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.

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