Calculation of general \(p\)-adic Feynman amplitude
type: Item
instance of: scholarly article
title: Calculation of general \(p\)-adic Feynman amplitude
zbMATH Open document ID: 0797.46058
DOI: 10.1007/BF02096946
published in: Communications in Mathematical Physics
publication date: 1993-01-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 81Q30
Mathematics Subject Classification ID: 11F85
zbMATH DE Number: 97877
zbMATH Keywords: \(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions
zbMATH Keywords: master two-loop diagram
zbMATH Keywords: star Feynman diagram
author: V. A. Smirnov
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97877