#### Top positive review

*5.0 out of 5 stars*The new standard

Reviewed in the United States 🇺🇸 on January 25, 2014

Short version: overall, this is the best QFT textbook available right now. It succeeds in covering a lot of ground without sacrificing accessibility. It is up to date and has some great exercises. It is also rare in that many derivations are worked out explicitly. If you are (relatively) new to the subject and want to start learning QFT, this book is probably your best bet.

Longer version:

About the author: Matt Schwartz is a professor at Harvard, where he has taught a very popular introductory QFT course several times over the last few years. The first half of the book (Parts I through III) arose from lecture notes that he prepared for the class, and whose contents have therefore been thoroughly student-tested (full disclosure: I was one of the students who pored over every equation in those notes). The result is the most pedagogical introduction to QFT to date. With the new material in Parts IV and V, it presents all the topics covered in an intensive year-long course.

The exercises at the end of every chapter have also been student-tested and are for the most part very illuminating: you’ll be asked to perform illustrative calculations (the bread and butter of the subject), to explicitly derive relations from the chapter (to test your understanding) or to get some extra practice by expounding on some side topic. Either way, these exercises are a valuable resource and provide additional insight into the material (though beware: in the later chapters, some problems can be fiendishly difficult). Remember: as with any advanced subject, it is crucial that you work through some of the details on your own!

The strength of the presentation lies in the author’s style: Matt Schwartz is not afraid to walk you through derivations step by step and point out common misunderstandings. As a result the book often adopts a chatty style, more akin to a teacher talking to his students than to a dry and terse summary. At 900 pages, it is therefore longer than its competition, but for beginners I see this as a feature rather than a bug!

Some other great features: the book does not assume much in the way of prerequisites (aside from quantum mechanics and special relativity) and even includes a chapter on classical field theory. The explanation of Feynman diagrams is really clear and many examples are provided (the diagrams are numerous and beautifully typeset). The author introduces QED gradually by working his way through scalar QED first, which allows him to focus on some important points without the complications of spinors. Below are some comparisons to similar books out there:

- Peskin & Schroder: the standard QFT textbook (up to now!). The chapters are quite uneven in quality: though some are excellently written (e.g. the discussion on non-abelian gauge theory), others are quite obscure. The going is especially rough in the beginning: for instance, I remember trying to understand the discussion of LSZ in P&S and being completely lost before turning to Matt Schwartz’s much clearer explanation.

Some discussions in P&S have also become somewhat dated, while Schwartz’ book is completely up to date. It even includes a chapter on the spinor helicity formalism, the framework in which the recent work on scattering amplitudes is couched!

- A. Zee's QFT in a Nutshell: this is another favorite of mine, and a great read once you've learned the basics of the subject and are looking for a different viewpoint. It’s also useful for beginners who want to get to know the lay of the land. While this book offers good insights into the subject, it only works through a single computation in detail! A good companion to Schwartz’s book, then, but not a viable alternative.

- Tom Banks’s book: a very concise overview of the subject, but definitely inaccessible to beginners. Banks uses the Schwinger-Dyson equation from the start, but never really explains it. Head over to Chapter 14 of Matt Schwartz’s book to learn about it before even thinking about attacking Banks.

- Mark Srednicki’s book: this book starts at a higher level of abstraction and is great for a second look at QFT. Schwartz’s book is definitely better suited to the novice, however, as it offers a gentler introduction and is more hands on in its approach.

- Weinberg's 3 volumes: notoriously difficult to learn from, but still *the* reference for certain topics. Volume 1, in particular, does the best job of explaining the structure of QFT and why most of it was inevitable. Again, not the place to learn how to compute from, but a pleasure to read after having absorbed Schwartz’s treatment.

In summary, there are now quite a few QFT books available on the market, each with their own niche. Matt Schwartz’ book offers the best compromise in terms of accessibility vs completeness, and should therefore have the widest appeal.