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What Is a Quantum Field Theory?
Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians. Most pedagogical texts on QFT are geared toward budding professional physicists, however, whereas mathematical accounts are abstract and difficult to relate to the physics. This book bridges the gap. While the treatment is rigorous whenever possible, the accent is not on formality but on explaining what the physicists do and why, using precise mathematical language. In particular, it covers in detail the mysterious procedure of renormalization. Written for readers with a mathematical background but no previous knowledge of physics and largely self-contained, it presents both basic physical ideas from special relativity and quantum mechanics and advanced mathematical concepts in complete detail. It will be of interest to mathematicians wanting to learn about QFT and, with nearly 300 exercises, also to physics students seeking greater rigor than they typically find in their courses. Erratum for the book can be found at michel.talagrand.net/erratum.pdf.
756 pages, Hardcover
Published May 31, 2022
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August 11, 2023
This is a brutally honest book written by a great mathematician with quite a sense of humor.
1. Talagrand does not sweep anything under the rug (or when he does, he explicitly told you and explain why he did it).
2. There are a number of places in the book that cracked me up, it is full of subtle humors.
3. I know nothing about physics to speak of. I have to read Wheeler & Taylor's Spacetime Physics to learn SR while reading Part II of this book. But you can go through the book without knowing any serious physics. The book treats QM as a mathematical formalism which I find helpful. So the author did not lie when he told you about the prerequisites for the book (which is so rare among math/physics book writers nowadays)
4. You need a solid background in Linear Algebra and Calculus (when in doubt, integrate by parts huh), and probably should have heard of what a Banach space is. But the rest of the math can be slowly (but surely) picked up from the appendix.
5. This is a extremely personal work for Talagrand and it shows. He made a huge effort to not just explain this stuff to himself but also to someone a lot weaker in math than him (yours truly). The resulting work reads almost like a notebook of mathematical thought process and it explain not only the formalism but also "where does this s**t come from in the first place"?
6. If you email the author about your questions and comments, he will reply promptly with helpful suggestions. There is an errata on his website which is also helpful.
7. I'm going to read it again soon. There are so many things I feel I can understand better on a second read.
1. Talagrand does not sweep anything under the rug (or when he does, he explicitly told you and explain why he did it).
2. There are a number of places in the book that cracked me up, it is full of subtle humors.
3. I know nothing about physics to speak of. I have to read Wheeler & Taylor's Spacetime Physics to learn SR while reading Part II of this book. But you can go through the book without knowing any serious physics. The book treats QM as a mathematical formalism which I find helpful. So the author did not lie when he told you about the prerequisites for the book (which is so rare among math/physics book writers nowadays)
4. You need a solid background in Linear Algebra and Calculus (when in doubt, integrate by parts huh), and probably should have heard of what a Banach space is. But the rest of the math can be slowly (but surely) picked up from the appendix.
5. This is a extremely personal work for Talagrand and it shows. He made a huge effort to not just explain this stuff to himself but also to someone a lot weaker in math than him (yours truly). The resulting work reads almost like a notebook of mathematical thought process and it explain not only the formalism but also "where does this s**t come from in the first place"?
6. If you email the author about your questions and comments, he will reply promptly with helpful suggestions. There is an errata on his website which is also helpful.
7. I'm going to read it again soon. There are so many things I feel I can understand better on a second read.
Displaying 1 of 1 review