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An Introduction to Non-Perturbative Foundations of Quantum Field Theory (International Series of Monographs on Physics) Hardcover – 14 Feb 2013

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This is the book many mathematically inclined theoretical physicists and physics-oriented mathematicians have been waiting for; an introductory textbook on quantum field theory and its applications written by theoretical physicist F. Strocchi, a world expert on the mathematical foundations of relativistic quantum field theory, working in this field himself for decades and having made profound contributions of research results. His book is the answer to the question students or researchers often ask: "Which book would you recommend to learn about quantum field theory?" (Volker Bach, Technische Universität Braunschweig)

Strocchi's book is an immensely valuable addition to the introductory literature on quantum field theory. It will be useful to physicists, mathematicians, and philosophers of physics alike, as it successfully bridges the gap between the rigorous and the non-rigorous, the formal and the heuristic approaches to quantum field theory. Those looking for a mathematically well-founded approach to the theories combined in the Standard Model of elementary particle physics can hardly do better than consult Strocchi's work. (Simon Friederich, Universität Göttingen)

This excellent new book presents the fundamental concepts of quantum field theory at a more mathematical and rigorous level than found in the many standard graduate texts in the field. It will be a valuable reference for particle physicists and others seeking a deeper understanding of the theoretical foundations of the standard model. (Graham Shore, Swansea University)

About the Author

Franco Strocchi is Senior Research Fellow at INFN. He received his Laurea in Physics at the University of Pisa and Diploma in Physics at Scuola Normale Superiore, Pisa (1961). He has taught as Professor of Theoretical Physics at SISSA, Trieste (1983-1994), and as Professor of Theoretical Physics at Scuola Normale Superiore (1994-2009). His main research interests include the theory of quantized fields and spontaneous breaking of symmetries.

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8 of 8 people found the following review helpful
5.0 out of 5 stars Excellent, up to date, authoritative and complete 23 Sept. 2013
By Gerald Kaiser - Published on
Format: Hardcover Verified Purchase
Quantum field theory (QFT) is a theory of elementary particles combining quantum mechanics and special relativity. The synthesis of these two is far from straightforward. In fact, the synthesis of quantum mechanics and *general* relativity, known as 'quantum gravity,' is still an open problem. Excluding string theory, on which the jury is still out, QFT is the most fundamental and comprehensive theory of physics today, encompassing all known physics except gravity. (Questions related to the recent discovery of the Higgs Boson had to be analyzed using QFT, as string theory proved to be of little help with specifics.) It is therefore not surprising that there is a huge number of books on the subject. However, due to the great difficulty of making reliable calculations, most such books contain many 'formal' equations which are widely understood to lack mathematical sense. Frequently such difficulties are due to the use of perturbation theory with questionable convergence properties. In the 1950s, work began by A. S. Wightman, L. Garding, R. Jost, R. Haag and others to base the theory on a few fundamental principles (axioms) and derive as much of the physics as possible from these principles by rigorous mathematical arguments without using perturbation methods. This approach, known as `axiomatic QFT,' has turned out to be very fruitful. In the 1970s it resulted in a proof of the complete equivalence between QFT and its imaginary-time counterpart, known as `Euclidean QFT' because the imaginary time is indistinguishable from the three (real) space dimensions, so that relativistic spacetime becomes simplified to four-dimensional Euclidean space. The `weirdness' of special relativity (where time behaves like an imaginary space dimension) and the weirdness of quantum mechanics (where observables do not commute, hence their measurements interfere) seem to "cancel" and become subsumed in a theory of random (probabilistic) classical (commuting) fields in four-dimensional Euclidean space. In this realm, rigorous non-perturbative computations can be performed and then mapped to the corresponding results in relativistic spacetime. This approach, known as `constructive QFT,' is a deep validation of the axiomatic method.

Due partly to the great popularity of string theory, only a handful of books on rigorous (axiomatic and constructive) QFT have appeared since the 1980s. Franco Strocchi's book is the latest, and one of the best. It is written with great care and clarity. Furthermore, it brings the rigorous approach to topics of current interest such as the infrared problem, the Higgs mechanism, and the theta vacua in Quantum Chromodynamics, which often suffer from mathematical inconsistencies in the standard textbooks. It is also an excellent text for self-study. I highly recommend it.
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