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Perturbative algebraic quantum field theory = an introduction for mathematicians /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Perturbative algebraic quantum field theory/ by Kasia Rejzner.
Reminder of title:	an introduction for mathematicians /
Author:	Rejzner, Kasia.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xi, 180 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Quantum field theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-25901-7
ISBN:	9783319259017

Perturbative algebraic quantum field theory = an introduction for mathematicians /
Rejzner, Kasia.

Perturbative algebraic quantum field theoryan introduction for mathematicians /[electronic resource] :by Kasia Rejzner. - Cham :Springer International Publishing :2016. - xi, 180 p. :ill., digital ;24 cm. - Mathematical physics studies,0921-3767. - Mathematical physics studies..

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 -- Kahler 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.

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. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. 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 QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience.

ISBN: 9783319259017

Standard No.: 10.1007/978-3-319-25901-7doiSubjects--Topical Terms:

579915
Quantum field theory.

LC Class. No.: QC174.45

Dewey Class. No.: 530.153

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505 0 $a 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 -- Kahler 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.
520 $a 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. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. 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 QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience.
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