What Is a Quantum Field Theory?
A First Introduction for Mathematicians
2nd Edition
Will be published approx. on 30. November 2026
Book
Paperback/Softback
814 pages
978-1-009-61975-2 (ISBN)
Description
Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians, yet standard texts often assume a physicist's background or adopt an abstract mathematical perspective. This thoroughly updated edition bridges that gap. While maintaining a rigorous approach wherever possible, it focuses on explaining what physicists do and why, using precise mathematical language. Written for readers with a background in mathematics but no prior knowledge of physics, and largely self-contained, it presents both essential physical ideas and the necessary mathematical tools in detail. This revised edition has been improved throughout, with many clarifications to the text and the inclusion of solutions to selected exercises to enhance its use for self-study. It will appeal to mathematicians seeking an accessible path into QFT and to physics students wanting greater rigor.
More details
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
ISBN-13
978-1-009-61975-2 (9781009619752)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Michel Talagrand has received the Loeve Prize, the Fermat Prize, the Shaw Prize and the Abel Prize. He was a plenary speaker at the International Congress of Mathematicians and is currently a member of the Academie des Sciences (Paris). He has written several books in probability theory and well over 200 research papers.
Content
Part I. Basics: 1. Preliminaries; 2. Basics of non-relativistic quantum mechanics; 3. Non-relativistic quantum fields; 4. The Lorentz group and the Poincare group; 5. The massive scalar free field; 6. Quantization; 7. The Casimir effect; Part II. Spin: 8. Representations of the orthogonal and the Lorentz group; 9. Representations of the Poincare group; 10. Basic free fields; Part III. Interactions: 11. Perturbation theory; 12. Scattering, the scattering matrix and cross-sections; 13. The scattering matrix in perturbation theory; 14. Interacting quantum fields; Part IV. Renormalization: 15. Prologue: power counting; 16. The Bogoliubov-Parasiuk-Hepp-Zimmermann scheme; 17. Counter-terms; 18. Controlling singularities; 19. Proof of convergence of the BPHZ scheme; Part V. Complements: A. Complements on representations; B. End of proof of Stone's theorem; C. Canonical commutation relations; D. A crash course on Lie algebras; E. Special relativity; F. Does a position operator exist?; G. More on the representations of the Poincare group; H. Hamiltonian formalism for classical fields; I. Quantization of the electromagnetic field through the Gupta-Bleuler approach; J. Lippmann-Schwinger equations and scattering states; K. Functions on surfaces and distributions; L. What is a tempered distribution really?; M. Wightman axioms and Haag's theorem; N. Feynman propagator and Klein-Gordon equation; O. Yukawa potential; P. Principal values and delta functions; Solutions to selected exercises; Reading suggestions; References; Index.