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

Format:

Book

Author/Creator:

Herscovich, Estanislao, author.

Series:

Astérisque ; 412.

Astérisque ; 412

Language:

English

French

Subjects (All):

Quantum field theory.

Renormalization group.

Renormalization (Physics).

Feynman diagrams.

Physical Description:

xvi, 185 pages ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, [2019]

Language Note:

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.

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.

Notes:

Includes bibliographical references (pages 175-182) and index.

ISBN:

9782856299104

2856299105

OCLC:

1110579338