---
product_id: 439804060
title: "What Is a Quantum Field Theory?"
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---

# What Is a Quantum Field Theory?

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Review: Accessible and Demystifying - I am a layman in both math and physics, self‑studying QFT with this book alongside Introduction to Quantum Field Theory by Anthony Williams. I’ve read carefully up to Chapter 6. This book serves as a reliable self‑learning guide—partly because it is the product of an esteemed mathematician’s own self‑study. As the author notes, it began as "an attempt to rewrite Folland's textbook" during his study of QFT. Talagrand is kind to the reader: he assumes little in the way of prerequisites and builds steadily. His candid, self‑deprecating humor is relatable too—for example, "To top it all, I was buried by the worst advice I ever received: to learn the topic from Dirac's book itself." I have enjoyed studying Chapter 3 (Non‑relativistic Quantum Field), which offers a clean progression that actually feels learnable: tensor products of Hilbert spaces → symmetrization → boson Fock space → universe in a box → quantization. Each step is clear with careful exposition, especially the part on the number basis. By putting the mathematical structure front and foremost, it reduces the mystery around QFT. I also appreciated Talagrand’s clarifications of the physicists’ point of view. A telling example appears on p. 99: when physicists say “attaching a harmonic oscillator to each point of space,” what’s really meant is one attached to each point in the set of allowable momenta. These translations clarify common slogans. The same can be said of his exposition of group theory (Appendix D). The balance between the physics and math perspectives makes the book approachable and provides a solid footing in a subject many find challenging. I believe it provides a foundation for tackling the standard textbooks (Peskin & Schroeder, Zee, Weinberg). It is accessible even to a layman and useful for physics students who want a healthy dose of the mathematical perspective.
Review: A T0 book on Quantum Field Theory for mathematics students - I am a PhD student in mathematics. In order to prepare for my doctoral ABD defense in August, I began studying the connections between quantum field theory (QFT) and statistical mechanics last year. I looked for many books on QFT for self-study, but most of them were not very accessible — they either assume an extremely strong background in mathematics or an equally strong background in physics. Michel’s book is different. It doesn’t require much prior knowledge; it starts from a level that is basic enough for me and gradually introduces the main ideas of quantum fields. To be honest, I haven’t finished reading the entire book yet, but I have already found in it the answers I was looking for — what QFT really is, and more importantly, where it comes from. The book covers a wide range of topics in quantum field theory. My suggestion for first-time readers is simply to focus on understanding what QFT is; the details can be filled in later during subsequent readings.

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #894,340 in Books ( See Top 100 in Books ) #107 in Waves & Wave Mechanics (Books) #357 in Mathematical Physics (Books) #625 in Physics (Books) |
| Customer Reviews | 4.8 4.8 out of 5 stars (32) |
| Dimensions  | 7 x 1.75 x 10 inches |
| Edition  | New |
| ISBN-10  | 1316510271 |
| ISBN-13  | 978-1316510278 |
| Item Weight  | 3 pounds |
| Language  | English |
| Print length  | 756 pages |
| Publication date  | May 31, 2022 |
| Publisher  | Cambridge University Press |

## Images

![What Is a Quantum Field Theory? - Image 1](https://m.media-amazon.com/images/I/51ajZDHkmmL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ Accessible and Demystifying
*by J***I on November 2, 2025*

I am a layman in both math and physics, self‑studying QFT with this book alongside Introduction to Quantum Field Theory by Anthony Williams. I’ve read carefully up to Chapter 6. This book serves as a reliable self‑learning guide—partly because it is the product of an esteemed mathematician’s own self‑study. As the author notes, it began as "an attempt to rewrite Folland's textbook" during his study of QFT. Talagrand is kind to the reader: he assumes little in the way of prerequisites and builds steadily. His candid, self‑deprecating humor is relatable too—for example, "To top it all, I was buried by the worst advice I ever received: to learn the topic from Dirac's book itself." I have enjoyed studying Chapter 3 (Non‑relativistic Quantum Field), which offers a clean progression that actually feels learnable: tensor products of Hilbert spaces → symmetrization → boson Fock space → universe in a box → quantization. Each step is clear with careful exposition, especially the part on the number basis. By putting the mathematical structure front and foremost, it reduces the mystery around QFT. I also appreciated Talagrand’s clarifications of the physicists’ point of view. A telling example appears on p. 99: when physicists say “attaching a harmonic oscillator to each point of space,” what’s really meant is one attached to each point in the set of allowable momenta. These translations clarify common slogans. The same can be said of his exposition of group theory (Appendix D). The balance between the physics and math perspectives makes the book approachable and provides a solid footing in a subject many find challenging. I believe it provides a foundation for tackling the standard textbooks (Peskin & Schroeder, Zee, Weinberg). It is accessible even to a layman and useful for physics students who want a healthy dose of the mathematical perspective.

### ⭐⭐⭐⭐⭐ A T0 book on Quantum Field Theory for mathematics students
*by C***I on October 23, 2025*

I am a PhD student in mathematics. In order to prepare for my doctoral ABD defense in August, I began studying the connections between quantum field theory (QFT) and statistical mechanics last year. I looked for many books on QFT for self-study, but most of them were not very accessible — they either assume an extremely strong background in mathematics or an equally strong background in physics. Michel’s book is different. It doesn’t require much prior knowledge; it starts from a level that is basic enough for me and gradually introduces the main ideas of quantum fields. To be honest, I haven’t finished reading the entire book yet, but I have already found in it the answers I was looking for — what QFT really is, and more importantly, where it comes from. The book covers a wide range of topics in quantum field theory. My suggestion for first-time readers is simply to focus on understanding what QFT is; the details can be filled in later during subsequent readings.

### ⭐⭐⭐⭐⭐ Brutally honest physics book written for mathematicians, full of hidden gems.
*by M***X on August 10, 2023*

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 treat QM as a mathematical formalism which I find helpful. 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). But the rest of the math can be slowly (but surely) picked up from the appendix. 5. This is an extreme personal work for Talagrand and it shows, and it is such a joy to read, especially his comments between the maths. 6. If you email the author about your questions, he will reply promptly with helpful comments. 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.

## Frequently Bought Together

- What Is a Quantum Field Theory?: A First Introduction for Mathematicians
- Quantum Theory for Mathematicians
- Quantum Field Theory: A Tourist Guide for Mathematicians (Mathematical Surveys and Monographs)

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