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...