Calculation of general \(p\)-adic Feynman amplitude
The general \(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions is calculated. First, the cases of two- and three-point Feynman amplitudes are considered, and the results are then generalized for arbitrary \(n\)- point amplitudes. The Feynman amplitude is written as a sum over hierarchies of the set of vertices of the given graph. These results are applied to simplest cases: the master two-loop diagram and the star Feynman diagram with three external and one internal vertices. Ultra- violet and infrared divergences of Feynman amplitudes are also analyzed. It is concluded that in the massless case, the \(p\)-adic Feynman amplitude can possess only logarithmical ultraviolet and infrared divergences.
\(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions
scientific article; zbMATH DE number 97877