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.
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.
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.
Inhaltsangabe
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.
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.
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