Mathematical Aspects of Quantum Field Theories

  • Damien Calaque
  • Thomas Strobl

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Locality in Perturbative QFTs

    1. Front Matter
      Pages 15-15
    2. Klaus Fredenhagen, Katarzyna Rejzner
      Pages 17-55
    3. Kevin Costello, Claudia Scheimbauer
      Pages 57-87
    4. Katrin Wendland
      Pages 89-129
  3. Chern–Simons Theory

    1. Front Matter
      Pages 131-131
    2. Jørgen Ellegaard Andersen, Rinat Kashaev
      Pages 133-152
    3. Domenico Fiorenza, Hisham Sati, Urs Schreiber
      Pages 153-211
    4. Nikita Markarian, Hiro Lee Tanaka
      Pages 213-231
  4. (Semi-)Classical Field Theories

    1. Front Matter
      Pages 273-273
    2. Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
      Pages 275-324
    3. Giuseppe Bonavolontà, Alexei Kotov
      Pages 325-341
  5. Algebraic Aspects of Locality

    1. Front Matter
      Pages 427-427
  6. Back Matter
    Pages 553-556

About this book


Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research.

This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed.

Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments.

This volume consists of four parts:
The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.


Chern-Simons Theory Factorization Algebras Factorization Homology Frobenius Algebras Grupoids Perturbative Quantum Field Theories Quantum Teichmueller Theory Supersymmetric Gauge Theories Topological Field Theories Witten-Reshetikhin-Turaev Invariants

Editors and affiliations

  • Damien Calaque
    • 1
  • Thomas Strobl
    • 2
  1. 1.Université Montpellier 2MontpellierFrance
  2. 2.Université Claude Bernard Lyon 1Villeurbanne CedexFrance

Bibliographic information