What Is a Quantum Field Theory?

Michel Talagrand

756 pages, parution le 16/03/2022

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Résumé

This introduction to the main ideas of quantum field theory (QFT) is written for readers with knowledge of undergraduate mathematics but no previous background in physics, focusing on in-depth understanding of the methods and concepts used by physicists, including renormalization, rather than experimental aspects of the theory.Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians. Most pedagogical texts on QFT are geared toward budding professional physicists, however, whereas mathematical accounts are abstract and difficult to relate to the physics. This book bridges the gap. While the treatment is rigorous whenever possible, the accent is not on formality but on explaining what the physicists do and why, using precise mathematical language. In particular, it covers in detail the mysterious procedure of renormalization. Written for readers with a mathematical background but no previous knowledge of physics and largely self-contained, it presents both basic physical ideas from special relativity and quantum mechanics and advanced mathematical concepts in complete detail. It will be of interest to mathematicians wanting to learn about QFT and, with nearly 300 exercises, also to physics students seeking greater rigor than they typically find in their courses.Introduction; 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.Michel Talagrand is the recipient of the Loeve Prize (1995), the Fermat Prize (1997), and the Shaw Prize (2019). 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.

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Michel Talagrand
Parution	16/03/2022
Nb. de pages	756
EAN13	9781316510278

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What Is a Quantum Field Theory?

Résumé

Caractéristiques techniques

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