Infrared catastrophe in a massless Feynman function
type: Item
instance of: scholarly article
title: Infrared catastrophe in a massless Feynman function
zbMATH Open document ID: 0809.46088
author: Takahiro Kawai
author: Henry P. Stapp
publication date: 1994-11-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75038
review text: A new kind of infrared catastrophe is discussed. Like the traditional infrared divergence it is a problem at the level of the amplitude not the probability. It arises from inserting an internal photon line into a Feynman diagram having no external charged-particle lines. The resulting Feynman function is well defined, but the small \(k\)-contributions convert the normal singularity along the Landau-Nakanishi singularity surface to a singularity of stronger kind [cf. \textit{L. D. Landau}, Nuclear Phys., 13, 183-192 (1959); \textit{N. Nakanishi}, Prog. Theor. Phys., 22, 128-144 (1959)]. This stronger singularity is incompatible with the known fall- off properties of charged particle propagators at large distances. This situation is examined in a concrete situation, with emphasis on the microlocal aspect. Although the microlocal simplicity of a holonomic system which characterizes a Feynman function is widely observed in the massive case, such simplicity can be destroyed by the insertion of a massless line.
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 81T18
Mathematics Subject Classification ID: 32S40
Mathematics Subject Classification ID: 81V10
zbMATH DE Number: 683170
zbMATH Keywords: infrared catastrophe
zbMATH Keywords: Feynman diagram having no external charged-particle lines
zbMATH Keywords: Landau-Nakanishi singularity surface
zbMATH Keywords: microlocal simplicity of a holonomic system
MaRDI profile type: Publication
OpenAlex ID: W2322599964
Wikidata QID: Q103399028
cites work: Q3743663
cites work: Discontinuity formula and Sato's conjecture
cites work: Q3479047
cites work: Mass Singularities of Feynman Amplitudes
cites work: On analytic properties of vertex parts in quantum field theory
cites work: Ordinary and Anomalous Thresholds in Perturbation Theory
DOI: 10.5802/AIF.1374
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 683170