Distributional limits of renormalized Feynman integrals with zero-mass denominators
type: Item
instance of: scholarly article
title: Distributional limits of renormalized Feynman integrals with zero-mass denominators
zbMATH Open document ID: 0323.46069
DOI: 10.1007/BF01609352
author: J. H. Lowenstein
author: E. R. Speer
published in: Communications in Mathematical Physics
publication date: 1976-01-01T00:00:00Z
review text: Within the Bogolyubov--Parasyuk--Hepp--Zimmermann framework of renormalized perturbation theory, the connected Green functions of quantum fields are expressed as sums of contributions from Feynman diagrams, each of which corresponds to an integral \[ T_\varepsilon(p)=\int d^{4m}k R_\varepsilon(p_1,\dots,p_n; \, k_1,\dots,k_m). \] The authors show that if the integral \[ T_\varepsilon(\varphi)=\int d^{4m}k d^{4n}p\varphi(n)R_\varepsilon(p;k) \] converges absolutely for every \(\varepsilon >0\) and \(\varphi\) in the Schwartz space of test functions \(\mathcal S(\mathbb R^{4n})\), then \(T_\varepsilon\) approaches, when \(\varepsilon\) tends to zero, a Lorentz invariant limit as a tempered distribution. This theorem generalizes previous results of Hepp and Zimmermann to cases where some or all of the mass parameters vanish.
Mathematics Subject Classification ID: 81T18
Mathematics Subject Classification ID: 81T17
Mathematics Subject Classification ID: 46T12
zbMATH DE Number: 3505653
MaRDI profile type: Publication
cites work: Q3261267
cites work: Proof of the Bogoliubov-Parasiuk theorem on renormalization
cites work: Convergence of Bogoliubov's method of renormalization in momentum space
cites work: Convergence theorems for renormalized Feynman integrals with zero-mass propagators
cites work: Resolution of Singularities and Division of Distributions
description: scientific article; zbMATH DE number 3505653