Renormalization in quantum field theory (after R. Borcherds) /

Renormalization in quantum field theory (after R. Borcherds) /

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Bibliographic Details
Author / Creator:	Herscovich, Estanislao, author.
Imprint:	Paris : Société Mathématique de France, [2019] ©2019
Description:	xvi, 185 pages ; 24 cm
Language:	English
Series:	Astérisque ; 412 Astérisque ; 412.
Subject:	Quantum field theory. Renormalization group. Renormalization (Physics) Feynman diagrams.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11925601

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ISBN:	9782856299104 2856299105
Notes:	Includes bibliographical references (pages 175-182) and index. In English, with abstracts in English and French.
Summary:	The aim of this manuscript is to provide a complete and precise formulation of the renormalization picture for perturbative Quantum Field Theory (pQFT) on general curved spacetimes introduced by R. Borcherds in [R. E. Borcherds, "Renormalization and quantum field theory", Algebra number theory 5 (2011) 627-658]. More precisely, we give a full proof of the free and transitive action of the group of renormalizations on the set of Feynman measures associated with a local precut propagator, and that such a set is nonempty if the propagator is further assumed to be manageable and of cut type. Even though we follow the general principles laid by Borcherds in loc. cit., we have in many cases proceeded differently to prove his claims, and we have also needed to add some hypotheses to be able to prove the corresponding statements. [page 4 of cover].

Table of Contents:

Preliminaries on algebra and functional analysis
Preliminaries on vector bundles
Some results on tensor products
Preliminaries on distributions on manifolds
Quantum field theory (after Borcherds)
The first main result: the simply transitive actions of the group of renormalizations
The second main result: the existence of a Feynman measure associated with a manageable local propagator of cut type.