Mathematics of Quantization and Quantum Fields

This book provides a comprehensive review of mathematical aspects of quantization and quantum field theory, covering canonical commutation and anti-commutation relations, free bosonic and fermionic fields, and interacting fields. It is essential reading for graduate students and researchers in mathematics and physics.

Format: Hardback
Length: 688 pages
Publication date: 09 February 2023
Publisher: Cambridge University Press

Quantum field theory is a fundamental branch of physics that describes the behavior of matter and energy at the atomic and subatomic levels. It is a complex and mathematical theory that requires a deep understanding of mathematics, including quantum mechanics, linear algebra, and differential equations. In this book, we will explore the mathematical aspects of quantum field theory, including the theory of quantum mechanics, quantum electrodynamics, and superstring theory. We will also discuss the applications of quantum field theory to various physical phenomena, such as the behavior of particles and the structure of the universe.

Quantum field theory is a fundamental branch of physics that describes the behavior of matter and energy at the atomic and subatomic levels. It is a complex and mathematical theory that requires a deep understanding of mathematics, including quantum mechanics, linear algebra, and differential equations. In this book, we will explore the mathematical aspects of quantum field theory, including the theory of quantum mechanics, quantum electrodynamics, and superstring theory. We will also discuss the applications of quantum field theory to various physical phenomena, such as the behavior of particles and the structure of the universe.

The mathematical structures underlying free bosonic or fermionic fields, such as tensors, algebras, Fock spaces, and CCR and CAR representations, are discussed in this book. These topics are essential for understanding the behavior of particles in quantum field theory and are applied to physical problems in later chapters.

Diagrammatics and the Euclidean approach to constructive quantum field theory are two important aspects of interacting fields that are covered in this book. Diagrammatics is a visual representation of the behavior of particles in quantum field theory, while the Euclidean approach is a mathematical framework for constructing quantum field theories.

This book is essential reading for graduate students and researchers in mathematics and physics. It provides a comprehensive and up-to-date review of the mathematical aspects of quantum field theory, including both basic and advanced topics. The book is well-written and accessible to students with a background in mathematics, and it includes numerous examples and exercises to help reinforce the concepts.

Since its first publication in 2013, this book has been widely recognized as a valuable resource for students and researchers in the field of quantum field theory. It has been reissued as an Open Access publication on Cambridge Core, making it accessible to a wider audience.

In conclusion, this book is a must-read for anyone interested in the mathematical aspects of quantum field theory. It provides a comprehensive and up-to-date review of the theory, including its mathematical structures, diagrammatics, and applications to physical problems. With its in-depth coverage, this text is essential reading for graduate students and researchers in mathematics and physics.

ISBN-13: 9781009290821