Quantum Field Theory and the Standard Model

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.

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!

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.

I was always interested in learning QFT but none of the available books (P&S, Srednicki, Zee's Nutshell) could offer me a clear understanding of the logic and reasoning behind QFT's esoteric formalism. That all changed after taking on Matthew Schwartz's book. There is so much to tell about this marvelous book, therefore I have thematically split my review into 5 sections below. Style of presentation: This is by far the most *congenial* (not for a lack of adjective) physics book I have taken on so far! The book adopts a refreshingly friendly and colloquial writing style (much like a tutor), calling out the big picture and emphasizing the important points in every discussion. It not only explains how the theory should work, but also how it should not, by pointing out the possible naive interpretations that a novice might make; Along the same line, the author keeps comparing the new topics with previous ones, in a non-repetitive way, each time shedding more light from a different angle, which helps bolster the core ideas in the reader's mind without overwhelming him/her, allowing the reader to make some profound conceptual connections. Intuition and depth: This is the most intuitive QFT book I have seen. Ideas that previously were merely mathematical equations became commonsense after being exposed to this book. Matthew Schwartz transcends the math beyond what is offered by the classic references in the field by adding his well-worded intuition, targeted at a graduate student. Just as a few examples from the first quarter of the book, the meanings of the commutation relations between the fields and their derivatives are beautifully tied to causality, the LSZ formula is demystified by making it responsible for generating the initial and final states, the essence of QFT interactions is concisely (and yet fully) presented (in only a few pages) through the Lagrangian derivation of the Feynman rules, prior to presenting the messier, yet more systematic Hamiltonian formulation, the guage-invariance and Ward identity are discussed in great depth through various illustrative examples, the discussion of various representations of the Lorentz and Poincare groups are quite unique, thanks to providing topological pictures and realistic numerical examples after building the math machinery, etc. Breadth: The multitude of topics covered is extensive, ranging from QFT and QED, to a complete treatment of the Standard Model, QCD and advanced topics such as background fields, heavy-quark physics, jets and effective theory. Moreover, each idea is presented/formulated through various approaches/methods, e.g. Feynman rules are derived in space mode and momentum mode using both Lagrangian and Hamiltonian approaches. Level, rigor, and notation: Without a doubt, this book (and frankly the whole subject) is intended to be taken up by a physics graduate student, although a talented senior undergraduate should also find the book useful. As for the mathematical rigor, I would describe it as "just enough", for a physics book. As far as notation, the author has been very careful not to confuse the reader by using excessive/abstruse notations; the author uses the modern conventions (first print is in 2014) and all the notations are clarified upon introduction. Necessary background: In order to really appreciate the book the reader should have a solid background in Quantum mechanics (Lagrangian and Hamiltonian formulations, spin, scattering, etc) and know the basics of Special theory of relativity, Electrodynamics, matrix algebra, multivariable calculus, and Complex integrals. As a final note, I should mention that the book has its own website, with a newly launched Forum section, where the author graciously answers readers' questions. Overall I really enjoy reading this book and highly recommend it.

I really love this book, it is the best quantum field theory (QFT) book I ever had. I especially like the author's discussions of the physical ideas behind those difficult and abstract concepts. For example, the Old-Fashioned Perturbation Theory (OFPT) is discussed in detail from the physical perspective. Through the introduction and the detailed calculation of the retarded propagator and advanced propagator, it presents to the readers a clear picture of OFPT and its major difference, pros and cons compared to the conventional QFT perturbation theory based on Feynman propagator. As far as I know there is no other QFT text available that presents OFPT with such great clarity. This book is a most updated modern introduction to QFT with illustrations, exercises and examples from recent theoretical and experimental results. For example, in the chapter discussing cross sections and decay rates, an experimental diagram from ATLAS collaboration 2013 at LHC showing the evidence for Higgs boson is used to illustrate the importance of cross section measurement. The best part of this book in my opinion is that, unlike many other QFT books, there are no esoteric and mysterious claims or statements made in the book, everything is clearly explained. For me, I have really learnt a lot of the stuff that I was unable to understand or grasp from other QFT books before. I just can't wait to complete the book so that I will then have a real full understanding of QFT and the standard model both conceptually and technically.

In my opinion, this is the best quantum field theory (QFT) book you want to learn from. If you are already an expert, there are better reference books for sure (and I own several of those.) However, I am not aware of a better book more suitable for a one-year introductory graduate course. (The class will probably will cover slightly more than half of the contents during that time.) Ideally, the entire book should be a four semester (or five or six quarter) course. It is neither too dry too mathematical and abstract, nor is it superficial, telling you things what they are without a detailed explanation. You will find many other books on QFT which will cover a specific topic better than Schwartz does. But overall, I have not seen one that is better rounded and better organized for the benefit of the student than this one. The focus of the book is the student, not a demonstration of the virtuosity of the author. This is clearly not meant to be a reference book, but equally clearly it makes an excellent text-book. For a yearlong introductory class on QFT, I highly recommend it.

Quantum Field Theory in a Nutshell This is an excellent book because of the fact after you finish it, it should be a joke to, read any book on OFT. I will advise you of this, you should almost, be an expert on the following and be able to do them like you can add 1+1: 1. Use Residues and the Residue Theorem, 2. Fourier Transforms, 3. Green's functions (at least enough exposure, you could solve a simple equation), 4. Quantum Mechanics (you should be comfortable with Dirac notation, |0> and so forth), 5. Lorentz transformations (I know it is only special rel. but I have found most students do not understand it as well as they think they do, for instance the momentum tensor), 6. This book is not a good place to try and learn about tensors. Finally, the Author of this book say's you only need a undergrad. understanding of QM. That is partially true but if you used Griffiths book you did not get much in the way of Dirac notation. This book should also not be taken, to be able to be understood by an advanced undergraduate. That, is the way Author's sell books ("Oh", you do not need to know a thing, this book will teach you all you need, that is never true). If the item's listed above are second nature to you, then you should have no problem's with this book. If you have access to Zee's OFT in a nutshell, read chapter one, Zee's book in not one of my favorites but you cannot beat chapter one for understanding how Feynman, came up with the ideas of his diagrams (this book is the only place I have seen it done in this detail). The Author has admitted that he has pulled, what he considered the best parts from other OFT books and put it into his book. So if you had about ten OFT books and knew what was the most understandable Chapters in those books, you would have this book. There are a few chapter where this book falls short and you might have trouble grasping the material. Over all he has chosen the best chapters from others books. This book is very understandable and I tutor students now and have found most of the material they can get form the book. It is always a super plus if you have access to someone that knows the material and can answer the questions you have or have a group you can study together with, to learn the material. Remember my opening sentence or you will not only be learning OFT, but other subjects at the same time and that is usually what makes OFT almost impossible to learn.

A great book to learn, review and/or get up to date on the present knowledge of QFT and the "Standard Model" ! While there are quite a few excellent QFT texts out there Professor Schwartz's book is an outstanding contribution to the list ! His style is quite thorough and yet is succinct and as clear as it is possible to cover a difficult (and convoluted) subject. As a result Professor Schwartz succeeds at covering (in a lot fewer pages) much more material than Coleman's (remarkable!) QFT "class notes" book. One drawback (that to be honest at first discouraged me from studying the book) is that his equations are "incomplete" in the sense that he does not fully (and/or accurately) document the "standard covariant/contravariant' indexing used my most ( all?) other widely used QFT texts. The advantage however is that the equations are quite easier to read and write down but it is up to the reader to verify that the equations are indeed "correct" and agree with the ones given in other standard texts. .