Perturbative Algebraic Quantum Field Theory An Introduction for Mathematicians

• Main Author: Rejzner, Kasia
• Format: eBook Book
• Language: English
• Published: Cham Springer Nature 2016; Springer; Springer International Publishing AG; Springer International Publishing
• Edition: 1
• Series: Mathematical Physics Studies
• Subjects: Field theory (Physics); Field Theory and Polynomials; Mathematical Physics; Physics; Physics and Astronomy; Quantum Field Theories, String Theory; Quantum field theory
• ISBN: 9783319259017; 3319259016; 3319258990; 9783319258997
• ISSN: 0921-3767; 2352-3905
• DOI: 10.1007/978-3-319-25901-7

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.