Table of contents

  1. Front Matter
    Pages I-XVI
  2. Frédéric Paugam
    Pages 1-29
  3. Mathematical Preliminaries

    1. Front Matter
      Pages 31-31
    2. Frédéric Paugam
      Pages 33-68
    3. Frédéric Paugam
      Pages 69-105
    4. Frédéric Paugam
      Pages 107-128
    5. Frédéric Paugam
      Pages 129-149
    6. Frédéric Paugam
      Pages 151-157
    7. Frédéric Paugam
      Pages 159-166
    8. Frédéric Paugam
      Pages 167-181
    9. Frédéric Paugam
      Pages 183-223
    10. Frédéric Paugam
      Pages 225-249
  4. Classical Trajectories and Fields

    1. Front Matter
      Pages 315-315
    2. Frédéric Paugam
      Pages 349-359
  5. Quantum Trajectories and Fields

    1. Front Matter
      Pages 361-361
    2. Frédéric Paugam
      Pages 363-374
    3. Frédéric Paugam
      Pages 403-409
    4. Frédéric Paugam
      Pages 411-424
    5. Frédéric Paugam
      Pages 425-442
    6. Frédéric Paugam
      Pages 443-448
    7. Frédéric Paugam
      Pages 449-467
  6. Back Matter
    Pages 469-487

About this book


The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature.
The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras. The book is primarily intended for pure mathematicians (and in particular graduate students) who would like to learn about the mathematics of quantum field theory.


81-02, 81T70, 81T13, 58A03, 58A20, 18-02, 18G55, 81T20, 81T17 category theory functional analysis functional geometry homotopical geometry quantum field theory and renormalization

Authors and affiliations

  • Frédéric Paugam
    • 1
  1. 1.Institut de Mathématiques de JussieuUniversité Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04563-4
  • Online ISBN 978-3-319-04564-1
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site
Industry Sectors
IT & Software
Consumer Packaged Goods
Energy, Utilities & Environment