What Is a Quantum Field Theory? - A First Introduction for Mathematicians

A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.

List of contents

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.

About the author

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

Summary

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.

Product details

• Authors: Michel Talagrand, Talagrand Michel
• Publisher: Cambridge University Press Academic
• Languages: English
• Product format: Hardback
• Released: 31.01.2022
• EAN: 9781316510278
• ISBN: 978-1-316-51027-8
• No. of pages: 756
• Dimensions: 180 mm x 255 mm x 45 mm
• Series: Print on Demand
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Miscellaneous; SCIENCE / Physics / Mathematical & Computational, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Mathematical physics, Mathematical / Computational / Theoretical physics