What Is a Quantum Field Theory?
Autor Michel Talagranden Limba Engleză Hardback – 16 mar 2022
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Specificații
ISBN-13: 9781316510278
ISBN-10: 1316510271
Pagini: 756
Dimensiuni: 174 x 250 x 42 mm
Greutate: 1.41 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States
ISBN-10: 1316510271
Pagini: 756
Dimensiuni: 174 x 250 x 42 mm
Greutate: 1.41 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States
Cuprins
Introduction; 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.
Recenzii
'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
'Talagrand has done an admirable job of making the difficult subject of quantum field theory as concrete and understandable as possible. The book progresses slowly and carefully but still covers an enormous amount of material, culminating in a detailed treatment of renormalization. Although no one can make the subject truly easy, Talagrand has made every effort to assist the reader on a rewarding journey though the world of quantum fields.' Brian Hall, University of Notre Dame
'A presentation of the fundamental ideas of QFT in a manner that is both accessible and mathematically accurate seems like an impossible dream. Well, not anymore! This book goes from basic notions to advanced topics with patience and care. It is an absolute delight to anyone looking for a friendly introduction to the beauty of QFT and its mysteries.' Shahar Mendelson, Australian National University
'I have been motivated to try and learn about quantum field theories for some time, but struggled to find a presentation in a language that I as a mathematician could understand. This book was perfect for me: I was able to make progress without any initial preparation, and felt very comfortable and reassured by the style of exposition.' Ellen Powell, Durham University
'In addition to its success as a physical theory, Quantum Field Theory (QFT) has been a continuous source of inspiration for mathematics. However, mathematicians trying to understand QFT must contend with the fact that some of the most important computations in the theory have no rigorous justification. This has been a considerable obstacle to communication between mathematicians and physicists. It is why despite many fruitful interactions, only very few people would claim to be well versed in both disciplines at the highest level. There have been many attempts to bridge this gap, each emphasizing different aspects of QFT. Treatments aimed at a mathematical audience often deploy sophisticated mathematics. Michel Talagrand takes a decidedly elementary approach to answering the question in the title of his monograph, assuming little more than basic analysis. In addition to learning what QFT is, the reader will encounter in this book beautiful mathematics that is hard to find anywhere else in such clear pedagogical form, notably the discussion of representations of the Poincaré group and the BPHZ Theorem. The book is especially timely given the recent resurgence of ideas from QFT in probability and partial differential equations. It is sure to remain a reference for many decades.' Philippe Sosoe, Cornell University
'a wonderful resource for anyone who wants to understand exactly what a quantum field theory is.' Peter Woit, Not Even Wrong blog
'Talagrand has done an admirable job of making the difficult subject of quantum field theory as concrete and understandable as possible. The book progresses slowly and carefully but still covers an enormous amount of material, culminating in a detailed treatment of renormalization. Although no one can make the subject truly easy, Talagrand has made every effort to assist the reader on a rewarding journey though the world of quantum fields.' Brian Hall, University of Notre Dame
'A presentation of the fundamental ideas of QFT in a manner that is both accessible and mathematically accurate seems like an impossible dream. Well, not anymore! This book goes from basic notions to advanced topics with patience and care. It is an absolute delight to anyone looking for a friendly introduction to the beauty of QFT and its mysteries.' Shahar Mendelson, Australian National University
'I have been motivated to try and learn about quantum field theories for some time, but struggled to find a presentation in a language that I as a mathematician could understand. This book was perfect for me: I was able to make progress without any initial preparation, and felt very comfortable and reassured by the style of exposition.' Ellen Powell, Durham University
'In addition to its success as a physical theory, Quantum Field Theory (QFT) has been a continuous source of inspiration for mathematics. However, mathematicians trying to understand QFT must contend with the fact that some of the most important computations in the theory have no rigorous justification. This has been a considerable obstacle to communication between mathematicians and physicists. It is why despite many fruitful interactions, only very few people would claim to be well versed in both disciplines at the highest level. There have been many attempts to bridge this gap, each emphasizing different aspects of QFT. Treatments aimed at a mathematical audience often deploy sophisticated mathematics. Michel Talagrand takes a decidedly elementary approach to answering the question in the title of his monograph, assuming little more than basic analysis. In addition to learning what QFT is, the reader will encounter in this book beautiful mathematics that is hard to find anywhere else in such clear pedagogical form, notably the discussion of representations of the Poincaré group and the BPHZ Theorem. The book is especially timely given the recent resurgence of ideas from QFT in probability and partial differential equations. It is sure to remain a reference for many decades.' Philippe Sosoe, Cornell University
'a wonderful resource for anyone who wants to understand exactly what a quantum field theory is.' Peter Woit, Not Even Wrong blog
Notă biografică
Descriere
A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.