Planar diagrams
type: Item
instance of: scholarly article
title: Planar diagrams
zbMATH Open document ID: 0997.81548
DOI: 10.1007/BF01614153
published in: Communications in Mathematical Physics
publication date: 2002-11-10T00:00:00Z
review text: The authors describe their method for counting planar Feynman diagrams of quantum field theory. Mathematicians who are not familiar with the current jargon of quantum field theory are likely to find this paper rather difficult to follow. In order to demonstrate the usefulness of their method, the authors calculate the ground state energy of a system of coupled anharmonic oscillators with a \(\phi^4\) interaction in the planar approximation. They obtain the value \(0.58993g^{1/3}\) in the limit of large \(g\), where \(g\) is the coupling constant. By comparing this with the value \(0.66799g^{1/3}\) which is described as exact, the authors conclude that the planar approximation is at most 12\% wrong!
Mathematics Subject Classification ID: 81T18
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 1825229
author: E. Brézin
author: C. Itzykson
author: G. Parisi
author: Jean-Bernard Zuber
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
cites work: A Census of Planar Triangulations
cites work: Q4221096
full work available at URL: https://doi.org/10.1007/bf01614153
OpenAlex ID: W4238712009
description: scientific article; zbMATH DE number 1825229