Perturbative Algebraic Quantum Field Theory

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.