© 2016

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


Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Kasia Rejzner
    Pages 1-2
  3. Kasia Rejzner
    Pages 3-37
  4. Kasia Rejzner
    Pages 39-58
  5. Kasia Rejzner
    Pages 59-81
  6. Kasia Rejzner
    Pages 83-93
  7. Kasia Rejzner
    Pages 137-156
  8. Kasia Rejzner
    Pages 157-171
  9. Back Matter
    Pages 173-180

About this book


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. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes.

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 QFT on curved spacetimes and effective quantum gravity.

The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience.


Batalin-Vilkoviski Formalism Epstein-Glaser Method Locally Covariant Quantum Field Theory Algebraic Quantum Field Theory Perturbative Quantum Field Theory Gauge Theory Mathematical Foundations of Quantum Field Theory Theory of Scalar field Quantum Field Theory on curved spacetimes Effective quantum gravity

Authors and affiliations

  1. 1.Department of MathematicsUniversity of YorkYorkUnited Kingdom

Bibliographic information


“The author, who claims to be both a physicist and a mathematician, offers a useful and fascinating book which should be of interest and useful to professional mathematicians and students of both mathematics and physics. It is dedicated to prominent mathematical physicists who passed away recently: Rudolf Haag, Daniel Kastler, Uffe Haagerup, Raymond Stora, and John Roberts ... . The book intends to be pedagogical and self-contained. It establishes the mathematical foundation of perturbation theory in a convincing manner.” (Gert Roepstorff, zbMATH 1347.81011, 2016)