Analyticity in quantum field theory I. The triangle graph revisited

Abstract

The leading singularity is studied in scalar triangle graphs. We observe that in some examples of practical interest like the « form factors » the anomalous singularity does not arise when we perform the momentum integrations in the Feynman-Stückelberg amplitudes, indicating that quantum field theory will not necessarily yield the so-called analytic scattering amplitudes. However, the analytic triangle form factor which shows the anomalous singularity and the corresponding Feynman-Stückelberg amplitude coincide everywhere above the normal thresholds, especially in the « physical region » of the variables. But we should be warned against the uncritical use of conventional methods and concepts, even in simple perturbation structures.