Integral Representations for Vertex Functions

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Abstract
The third‐order Feynman graph is studied as a function of the three external masses squared for arbitrary real values of the internal masses. Single and double ``dispersion'' relations are derived which, for arbitrary real values of the undispersed variable(s), involve integrations only over real contours. Tables list the spectral functions for both the single and double integral formulas. In several cases, a non‐Landau singularity (on the forward scattering curve) appears on the ``physical sheet'', but not as a singularity of the physical boundary value.