Perturbative Algebraic Quantum Field Theory
An Introduction for Mathematicians
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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. 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 beaccessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience.
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.
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: sn.pub/extras
Autor*in
Kasia Rejzner
Themen in »Perturbative Algebraic Quantum Field Theory«
Batalin-Vilkoviski Formalism Epstein-Glaser Method Locally Covariant Quantum Field Theory Algebraic Quantum Field Theory Perturbative Quantum Field Theory Gauge Theory Mathematical Foundations of Quantum Field Theory Theory of Scalar field Quantum Field Theory on curved spacetimes Effective quantum gravity
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“The author, who claims to be both a physicist and a mathematician, offers a useful and fascinating book which should be of interest and useful to professional mathematicians and students of both mathematics and physics. It is dedicated to prominent mathematical physicists who passed away recently: Rudolf Haag, Daniel Kastler, Uffe Haagerup, Raymond Stora, and John Roberts ... . The book intends to be pedagogical and self-contained. It establishes the mathematical foundation of perturbation theory in a convincing manner.” (Gert Roepstorff, zbMATH 1347.81011, 2016)
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