What Is a Quantum Field Theory? (Hardcover)

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.

量子場論（QFT）是物理學的一項偉大成就，對數學家來說具有深遠的興趣。大多數關於QFT的教材都針對新手專業物理學家，然而數學描述抽象且難以與物理相關聯。這本書彌補了這一差距。雖然在可能的情況下，對待是嚴謹的，但重點不在形式上，而在於解釋物理學家做什麼以及為什麼這樣做，使用精確的數學語言。特別是，它詳細介紹了修正的神秘程序。本書針對具有數學背景但沒有物理學先備知識的讀者，並且在很大程度上是自成一體的，它既介紹了特殊相對論和量子力學的基本物理思想，也詳細介紹了高級數學概念。對於想要了解QFT的數學家來說，這本書很有興趣，同時也對物理學生有興趣，他們在課程中通常找不到這種嚴謹性。書籍的勘誤表可以在michel.talagrand.net/erratum.pdf找到。