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# Quantum Field Theory and the Standard Model

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Review: The new standard - 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.
Review: This is the BEST of the Best in Books about Quantum Field Theory. A MUST BUY. Thumbs up! - I must have practically all books about QFT, some of them are quite good at specific tasks or subjects but not on all things they cover, for example, Ashok Das Lectures on QFT is very very good for Renormalization; or Greiner in the treatment of Wick's Theorem, Peskin in the treatment of One-Loop Feynman Diagrams like the self energy of the Electron, Vacuum Polarization and specially the treatment of the QED Vertex and the Anomalous magnetic moment of the electron using the Gordon identities and the Cutkovsky rules for the cut of the diagrams in the QFT version of the Optical Theorem (Conservation of Probability). Ryder is quite good as well for quantization of non-abelian Gauge field theories, or Hatfield and his unique treatment of QFT in the Schroëdinger picture. BUT if you want ONE just ONE book where you can see all of these (and save a lot of money! as well) BUY Matthew Schwartz Quantum Field Theory and the Standard Model, it is PERFECT although because lack of time I have only gone through parts 1 Field Theory & 2 Quantum Electrodynamics, (Has 5 parts in total) I remember that, from this book, I finally understood the "+ie" notation or prescription for the Feynman Propagator implying choosing the correct vacuum of the theory and causality of the propagator and actually how to get from the complex integral in 3 dimensions to the well known result in 4 dimensions which by the way my professor at my University (long time ago!) dinn't even bother to do it, he just said well from this 3 diomensional integral you can get to this result in 4 dimensions but offered us no clue at all, now actually here in Schwartzs IS DONE with full details. Well actually everything I have read is crystal clear and shows that when Scholars or better said Professors from the "Good" Universities like Schwartz from "Harvard" not only dedicate to write scientific articles, but use their expertise in writing books for, all the rest of us, then MAGIC happens! Also, there is another professor from Harvard who has written several books specially in Classical Mechanics and same thing happens i.e. MAGIC! again, this is, David Morin, I recommend his (Morin) books on Classical Mechanics, one in Probability, another on Special Relativity, and there are some notes on the internet for an unpublished work of him on Oscillations and Waves. Schwartz book is very complete after parts 1 & 2, comes Part 3: Renormalization, infrared divergencies (I learnt this stuff INFRARED, from the book of T. Muta "Foundations of Quantum Chromodynamics"), Unitarity, Part 4: Standard Model with Weak and Strong (QCD) interactions, covers jets, anomalies like the triangle one, anomaly matchings, gauge and global anomalies and Part 5: Advanced topics like, The Schwinger method, effective actions and background fields. A MUST HAVE for every High Energy Physicists. Thumbs up!

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #143,436 in Books ( See Top 100 in Books ) #4 in Particle Physics #30 in Physics (Books) #41 in Mathematical Physics (Books) |
| Customer Reviews | 4.6 out of 5 stars 265 Reviews |

## Images

![Quantum Field Theory and the Standard Model - Image 1](https://m.media-amazon.com/images/I/714dao22ndL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ The new standard
*by A***A 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.

### ⭐⭐⭐⭐⭐ This is the BEST of the Best in Books about Quantum Field Theory. A MUST BUY. Thumbs up!
*by R***A on March 30, 2024*

I must have practically all books about QFT, some of them are quite good at specific tasks or subjects but not on all things they cover, for example, Ashok Das Lectures on QFT is very very good for Renormalization; or Greiner in the treatment of Wick's Theorem, Peskin in the treatment of One-Loop Feynman Diagrams like the self energy of the Electron, Vacuum Polarization and specially the treatment of the QED Vertex and the Anomalous magnetic moment of the electron using the Gordon identities and the Cutkovsky rules for the cut of the diagrams in the QFT version of the Optical Theorem (Conservation of Probability). Ryder is quite good as well for quantization of non-abelian Gauge field theories, or Hatfield and his unique treatment of QFT in the Schroëdinger picture. BUT if you want ONE just ONE book where you can see all of these (and save a lot of money! as well) BUY Matthew Schwartz Quantum Field Theory and the Standard Model, it is PERFECT although because lack of time I have only gone through parts 1 Field Theory & 2 Quantum Electrodynamics, (Has 5 parts in total) I remember that, from this book, I finally understood the "+ie" notation or prescription for the Feynman Propagator implying choosing the correct vacuum of the theory and causality of the propagator and actually how to get from the complex integral in 3 dimensions to the well known result in 4 dimensions which by the way my professor at my University (long time ago!) dinn't even bother to do it, he just said well from this 3 diomensional integral you can get to this result in 4 dimensions but offered us no clue at all, now actually here in Schwartzs IS DONE with full details. Well actually everything I have read is crystal clear and shows that when Scholars or better said Professors from the "Good" Universities like Schwartz from "Harvard" not only dedicate to write scientific articles, but use their expertise in writing books for, all the rest of us, then MAGIC happens! Also, there is another professor from Harvard who has written several books specially in Classical Mechanics and same thing happens i.e. MAGIC! again, this is, David Morin, I recommend his (Morin) books on Classical Mechanics, one in Probability, another on Special Relativity, and there are some notes on the internet for an unpublished work of him on Oscillations and Waves. Schwartz book is very complete after parts 1 & 2, comes Part 3: Renormalization, infrared divergencies (I learnt this stuff INFRARED, from the book of T. Muta "Foundations of Quantum Chromodynamics"), Unitarity, Part 4: Standard Model with Weak and Strong (QCD) interactions, covers jets, anomalies like the triangle one, anomaly matchings, gauge and global anomalies and Part 5: Advanced topics like, The Schwinger method, effective actions and background fields. A MUST HAVE for every High Energy Physicists. Thumbs up!

### ⭐⭐⭐⭐ If you had to pick one QFT book, this is it
*by N***E on June 11, 2014*

Previously, I gave this book a five. However, there is one GLARING problem with this book. The author decided to completely ignore contra/covariance of indices. He states that one up, one down = two down = two up and the summation is in effect for all of these. For most cases, this is fine. But even a Harvard professor has instances in this book where he screws up thanks to this ambiguous notation and leads to mistakes. I've been confused a handful of times trying to decide what he meant. A Kronecker delta with two lower Lorentz indices...? Surely, this notation will just serve to confuse students. Especially when it comes to any other single book/article out there. I've never seen an author ignore index position. Why train students who should be close to publishing to break the rules? Besides that, this is probably the single best QFT I've found. Just to compare to the standards, we have Schwartz which starts you off slow and teaches you everything you need to know for QFT. Scalar fields, scattering, perturbation theory, everything. Have no fear using this book, if you made it half way through a grad QM course, you know enough to use it. Everything that this book covers is well explained and developed. P&S starts off and assumes classical field theory/complex scalar fields/canonical quantization of vector fields are trivial since birth and need no coverage. I didn't get very far in P&S, but there was nothing that I found myself saying "that was well developed." Completely opposite of Schwartz. Every section in Schwartz is impressing me. Srednicki covers these topics, but is MUCH more terse and formal. His mixing in of renormalization and counterterms to the first time development makes the book a much tougher pill to swallow. I feel as if Srednicki probably makes a better course textbook. Schwartz is a bit too slow and easy at times. If you are capable enough of a student to make it to a second year grad school QFT course, Schwartz might not be demanding enough. I feel that being pushed to understand all the terseness of Srednicki makes for a better physicist. That being said, Schwartz does such a good job of teaching, I believe that all students should have it anyways. It's the perfect companion to Srednicki. P&S has no place, in my opinion. P&S isn't hard, it just skips as much material as possible in order to get you to start being a robot that spits out Feynman diagram calculations. If I were to suggest a path to learning QFT to a new graduate student, I'd tell him to get Klauber early and read it to introduce you to the fundamentals. Get Schwartz to accompany your course. Hopefully your course uses Srednicki. Once you are done with the course, a more terse exposition such as Weinberg should be read to really understand what is going on. Zee to keep things fun in between.

## Frequently Bought Together

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