Perturbative Algebraic Quantum Field Theory: An Introduction for Mathematicians

A brief, though complete and self-consistent, introduction to perturbative Algebraic Quantum Field Theory (pAQFT)
Written by one of the leading experts in the field
The reader get all the prerequisites to understand QFT concepts used in cutting edge research in particle physics, cosmology and solid state physics.
A useful reference for mathematicians interested in QFT

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.