About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101316510271

ISBN-139781316510278

eBay Product ID (ePID)8050391385

Product Key Features

Number of Pages750 Pages

Publication NameWhat Is a Quantum Field Theory? : a First Introduction for Mathematicians

LanguageEnglish

SubjectPhysics / Mathematical & Computational, Physics / General

Publication Year2022

FeaturesNew Edition

TypeTextbook

AuthorMichel Talagrand

Subject AreaScience

FormatHardcover

Dimensions

Item Height1.7 in

Item Length9.8 in

Item Width6.9 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2021-020786

Dewey Edition23

Reviews'This book accomplishes the following impossible task. It explains to a mathematician, in a language that a mathematician can understand, what is meant by a quantum field theory from a physicist's point of view. The author is completely and brutally honest in his goal to truly explain the physics rather than filtering out only the mathematics, but is at the same time as mathematically lucid as one can be with this topic. It is a great book by a great mathematician.' Sourav Chatterjee, Stanford University, 'a wonderful resource for anyone who wants to understand exactly what a quantum field theory is.' Peter Woit, Not Even Wrong blog

IllustratedYes

Dewey Decimal530.143

Table Of ContentIntroduction; 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.

Edition DescriptionNew Edition

SynopsisQuantum 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. Erratum for the book can be found at michel.talagrand.net/erratum.pdf., 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.

LC Classification NumberQC174.45.T35 2021