Mathematics of Quantization and Quantum Fields

Unifying topics that are scattered throughout the literature, this book offers a definitive review of mathematical aspects of quantization and quantum field theory. It presents both basic and advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. It begins with a discussion of the mathematical structures underlying free bosonic or fermionic fields: tensors, algebras, Fock spaces, and CCR and CAR representations. Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in mathematics and physics. This title, first published in 2013, has been reissued as an Open Access publication on Cambridge Core.

• Unifies various aspects of quantization and quantum fields, encouraging a deeper understanding of some of the mathematical aspects of quantum field theory
• Fills a gap in the market by focusing on the mathematical aspects of QFT with a unique and consistent presentation
• Depth of coverage - the reader will find rigorous mathematical results
• This title has been reissued as an Open Access publication on Cambridge Core