What Is a Quantum Field Theory?

A First Introduction for Mathematicians

AvMichel Talagrand

Häftad, Engelska, 2026

588 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2026-11-30
Format:Häftad
Språk:Engelska
Antal sidor:814
Upplaga:2
Förlag:Cambridge University Press
ISBN:9781009619752

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Michel Talagrand has received the Loève 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 Académie des Sciences (Paris). He has written several books in probability theory and well over 200 research papers.

Innehållsförteckning

Part I. Basics: 1. Preliminaries; 2. Basics of non-relativistic quantum mechanics; 3. Non-relativistic quantum fields; 4. The Lorentz group and the Poincaré 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 Poincaré 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 Poincaré 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.