Mathematics – Logic
Scientific paper
Jun 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005cqgra..22.2533m&link_type=abstract
Classical and Quantum Gravity, Volume 22, Issue 12, pp. 2533 (2005).
Mathematics
Logic
Scientific paper
This new book on quantum field theory by Michele Maggiore fits well into the Oxford Master Series in Physics, which is designed for final year undergraduate and beginning graduate students in physics. It is based on the teaching experience of the author with students in the fourth year at the University of Geneva. In this sense it is a two-semester course book for students exposed to quantum field theory for the first time.
Maggiore gives, on slightly less than 300 pages, a balanced introduction to a vast field of twentieth century physics that will help students going on to study more advanced and specialized courses. Beside applications to many processes in particle physics that can also be found in many other textbooks, the author emphasizes conceptual, structural and methodological aspects of quantum field theory.
After an introductory chapter, the group theoretical tools required to implement Lorentz invariance in quantum field theory are developed on 30 pages. Chapter 3 is devoted to classical field theory, emphasizing symmetries and conservation laws. The quantization of free fields in the next chapter follows traditional lines. Here one may miss a section describing the mathematical structure of the Fock space. It is also not said that in infinite dimensions von Neumann's uniqueness theorem for the representations of the canonical commutation relations no longer holds. The operations C, P, T are carefully discussed. In the relatively long chapter 5, perturbation theory and renormalization are developed. In this context the author discusses the modern view on renormalizability, and also emphasizes in a separate section the seriousness of the cosmological constant problem in quantum field theory. The next three chapters provide applications of the theory, especially to quantum electrodynamics and the low-energy limit of the electroweak theory. Chapters 9, 10, and 11 are meant as a bridge to more advanced courses. In these, path integral quantization, non-Abelian gauge theories and spontaneous symmetry breaking receive a first treatment.
The book is very well structured. At the end of each chapter a summary is given and some of them contain an instructive 'Solved Problems' section. The many exercises posed in the first eight chapters are solved in a final chapter. This book by Michele Maggiore should become a standard text for a modern introduction to quantum field theory.
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