Perturbative Algebraic Quantum Field Theory

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Beschreibung

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn¿t require the use of divergent quantities and works on a large class of Lorenzian manifolds.
We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity.
pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems.
Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity.
The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Zusammenfassung

A brief, though complete and self-consistent, introduction to perturbative Algebraic Quantum Field Theory (pAQFT)

Written by one of the leading experts in the field

The reader get all the prerequisites to understand QFT concepts used in cutting edge research in particle physics, cosmology and solid state physics.

A useful reference for mathematicians interested in QFT

Includes supplementary material: [...]

Inhaltsverzeichnis

Introduction.- Algebraic approach to quantum theory.- Algebraic quantum mechanics.- Causality.- Haag-Kastler axioms.- pAQFT axioms.- LCQFT.- Kinematical structure.- The space of field configurations.- Functionals on the configuration space.- Fermionic field configurations.- Vector fields.- Functorial interpretation.- Classical theory.- Dynamics.- Natural Lagrangians.- Homological characterization of the solution space.- The net of topological Poisson algabras.- Analogy with classical mechanics.- Deformation quantization.- Star products.- The star product on the space of multivector fields.- Kähler structure.- Interaction.- Outline of the approach.- Scatering matrix and time ordered products.- Renormalization group.- Interacting local nets.- Explicit construction.- Gauge theories.- Classical gauge theory.- Gauge-fixing.- BV formalism.- Effective quantum gravity.- From LCQFT to quantum gravity.- Dynamics and symmetries.- Linearized theory.- Quantization.- Relational observables.- Background independence.

Details

Erscheinungsjahr:	2018
Fachbereich:	Theoretische Physik
Genre:	Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	192
Reihe:	Mathematical Physics Studies
Inhalt:	xi 180 S. 4 s/w Illustr. 180 p. 4 illus.
ISBN-13:	9783319798578
ISBN-10:	331979857X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Rejzner, Kasia
Auflage:	Softcover reprint of the original 1st ed. 2016
Hersteller:	Springer International Publishing Springer International Publishing AG Mathematical Physics Studies
Maße:	235 x 155 x 11 mm
Von/Mit:	Kasia Rejzner
Erscheinungsdatum:	24.04.2018
Gewicht:	0,3 kg

preigu-id: 114236073