Quantum Field Theory for the Gifted Amateur

I enjoyed this textbook quite a bit. If utilizing this text for self-study, be sure and visit the author's academic website where a list of errata can be found (most typos are minor and can be cleaned up with a bit of dimensional analysis: for instance, the -1/2 for lambda should be +1/2 on bottom of page 408. This highlights an issue regarding background: dimensional analysis can be incredibly helpful. For instance, you would not forget the (2*pi)^4 in the denominator of equation #24 (page 6) if you were simply to keep your eye on dimensions. Onward: (1) Mathematics prerequisite: Mary Boas, Mathematical Methods In The Physical Sciences (chapters two and eleven). Boas is necessary background. View page 285 of Lancaster and Blundell, three integrals at bottom of page--you either know them, or not. If not, review that material ! View appendix B of Lancaster and Blundell, a review of complex analysis. There are seven examples there. If those examples are not completely understandable, the material needs to be learned. Note: Anthony Zee's textbook, QFT In A Nutshell, will not review complex variables. Thus, it is already clear that this textbook is pitched at a lower plane than Zee's insightful textbook. (2) Complex variables, dimensional analysis, integration-by-parts, "resolution of the identity" these tools (and more) are your lifeblood. You surely want to recognize the difference between Lagrangians and Hamiltonians. It is difficult to recommend here a mechanics text. I will say this: my course in junior-level mechanics was inadequate when it came to either Lagrangians or Hamiltonians. I hope undergraduate instruction has since changed in that regard. In any event, recognize the difference between when derivatives are more useful as a tool, as opposed to when Integrals are more useful (That begs the question: Why did it take ever so long for the Feynman path integral techniques to become part and parcel of the establishment ? Read Kaiser.). (3) Let me survey the pedagogic attributes of this textbook: Margin notes amplify textual material, summaries at end-of-chapter, diagrams and figures (cartoons) along the way, many examples to ruminate upon, intermediate steps in the mathematical derivations supplied, and last (but not least) excellent problems for student involvement (hints for their solution, too. For instance, problem #35.2, verify the Gell-Mann-Low equations. Some exercises are relatively easy, for instance, problem #30.2,"suggest a form for (4+1)-dimensional Chern-Simons term". It is difficult to overstate this: (4) Do the exercises ! When I say an exercise is "relatively easy," I imply this: If you study what Lancaster and Blundell have written, if you study their examples thoroughly, if you perform intermediate calculations on your own, then those end-of- chapter exercises are within grasp ! I am unfamiliar with a textbook quite as elementary as is this one (and, I own almost the entire gamut of texts-- from 1959 to 2017-- I will say the pedagogy of Zee "of letting you discover the Feynman diagrams for yourself " is admirable (Zee, page 44, 2010); yet his text is for a different subset of learners. An exercise herein: "We'll work through a famous proof of Goldstone's Theorem--the states linked to the ground state via the Noether current are massless Goldstone modes." (see page 246, #26.3 parts a through g). Compare to Anthony Zee (page 228), although I very much like how Peskin and Schroeder approach the Goldstone Theorem (page 351). (5) Take a linguistic tour, reading what Lancaster and Blundell have to say: "commutation operators contain all the information about the states." (page 35) and "the formerly negative-energy-states are interpreted as positive-energy antiparticles with momenta in the opposite direction to the corresponding particle." (page 63), and, "to get around the infinity encountered at the end of the last section, we define the act of Normal Ordering." (page 105), and "it may be helpful to think of the freedom of the choice of gauge as a choice of language." (page 129). Reading: " a QFT which satisfies a fairly minimal set of assumptions--lorentz invariant, local, Hermitian and Normal Ordered--possesses the symmetry PCT." (page 139). Also, "propagators, with their 'from here to there definition', also have the appealing property that they can be drawn in a cartoon form showing a particle travelling from y to x. This isn't quite as trivial as it sounds." (page 150). Finally: "In this way of looking at the world, our theories of Nature are low-energy, effective field theories, which will eventually break down at high enough energies." (page 294). Each line quoted above is enhanced with plentiful detail within each chapter that you find it ! (6) Spin arrives late (chapter nine, page 321). Dirac equation arrives late. That strategy makes sense. We read from Steven Weinberg: "Dirac's original motivation for this equation as a sort of relativistic Schrodinger equation does not stand up to inspection." (Quantum Theory Of Fields, volume one, page 565). What Weinberg has to say is reinforced in more elementary terms here. Reiterating: Lancaster and Blundell pitch themselves at a more elementary vantage. (7) This review could go on forever ! For instance, the pedagogic approach to renormalization is multi-pronged, multi-chaptered. Instead of continuing, I will simply reiterate my view that this textbook is an excellent bridge for further excursions into quantum field theory. It is difficult to be objective: Anthony Zee's QFT In A Nutshell is hard to beat, but it is not truly an introduction (perhaps, though, if you are already brilliant). For those students who aspire to get there (brilliance, that is) Lancaster and Blundell provide an opportunity to approach the goal. (8) My favorite textbooks: Steven Weinberg for understanding (also, Anthony Duncan), Peskin and Schroeder for computation. However, for an elementary textbook, Lancaster and Blundell hit closest to the mark. You will want to utilize Shankar, Principles of Quantum Mechanics, for collaborative reading (for instance, regards coherent states). Before study of the book, view appendix B (complex analysis) and example #1.2 (page 13). Do they make sense ? If so, this text may be what you are looking for. If not, learn the material in the appendix, then return to these pages. This textbook is difficult to surpass, especially for a truly elementary and pedagogic textbook.

Fantastic book on QFT! Covers the basics very well. There are a lot of chapters (50) but they are all short (~10 pages each). I like the short chapters as it makes it easy to set reading goals (ex: 2 chapters a day) without having to figure out where to stop reading and yet still have a coherent reading schedule. I 100% recommend this book for those who want to learn the basics of QFT but are not aiming to be quantum field theorists. Of course those that are aiming to be quantum field theorists will also learn a lot from this book and I'd recommend reading this over the summer before taking your first QFT course, but you will obviously want to use this textbook as a stepping stone to the more advanced QFT textbooks out there. This book will give you a strong conceptual understanding of QFT and the book goes over basic/standard problems in QFT. A QFT course that uses Peskin and Schroeder or the like will then help you fill in the details and do more advanced problems, but you'll have a solid grasp after reading QFT for the Gifted Amateur. Now, the title itself is pretty lame, in my opinion. The "for the Gifted Amateur" part is uninformative and potentially misleading and, if nothing else, just corny. Should you buy this book? Are you a "gifted amateur" (ill-defined term)? Well.... If this is you, then the text book is perfect for you: 0) You know close to nothing about QFT. 1) You've had a course on classical mechanics that covered the Lagrangian and the Hamiltonian formalism. 2) You've had a course on quantum mechanics, preferably graduate level. Basically, you should ideally be at the level of Shankar/Sakurai quantum mechanics. 3) You know undergraduate electromagnetism (Griffiths is fine). You should ideally be exposed to the electromagnetic field tensor F_{uv}, but this isn't hard to learn on your own. Knowing graduate level electromagnetism is even better, but an overkill for this textbook. 4) You should know the basics of tensor notation. (The first two chapters of Sean Carroll's general relativity book should do the trick.) So you should know what things like g_{uv}a^{u}b^{v} mean and not get scared by stuff like that. 5) You are comfortable with basic Fourier transforms. Knowledge of Laplace transforms would be helpful if you want to solve some of the more involved exercises, but isn't really a prerequisite. 6) You know basic complex analysis. Just the typical undergraduate course on complex analysis will suffice. So Cauchy's theorem, residue theorem, and contour integration. You don't need to be an expert by any means, but knowing the basics will let you follow some steps in some of the equations involving integrals or poles. In my opinion, the ideal reader would meet these qualifications and would benefit greatly from reading this textbook and should not have terrible difficulties in the reading process. There are probably more prerequisites that would be helpful, but these are probably the most important. Any other prerequisites can be self-taught if the reader runs into a chapter or exercise that has some basic concepts he/she does not understand. To repeat: This book is NOT a "I want to learn QFT but I'm not very good at math and I didn't like physics when I was in school but I love knowledge and I am a gifted amateur!" It's not a book for the masses in the sense that you love reading books and learning stuff. This is a legit physics textbook. The standard QFT textbooks are usually dense, really advanced and focus a lot on the small details, or some combination thereof. This book bridges the gap between the level of not knowing any QFT and the level of the standard QFT textbooks.

Updated after several months. This is an outstanding first book for QFT. There are several more advanced topics such as the LSZ reduction formula that would have been great to have, but for a first go this is the best I have found. I found it much more comprehensible than another intro book "A Student Friendly Introduction to QFT". If you get this book and work through it during the summer before your first QFT course, you should be way ahead. Original Review: The flow of the book is excellent. I would suggest that the "gifted amateur" is probably someone who has taken a "Modern Physics" course at the sophomore/junior college level. Otherwise a review of quantum mechanics at either that level or the level of Griffiths excellent quantum book should be undertaken first. For the most part the book flows very well with a well-paced development of field theory, why we need one, and creation and annihilation operators. The authors are condensed matter experimentalists, which means that the book does not assume that you are going to do particle physics theory soon. There are many examples drawn from condensed matter that are excellent. Feynman diagrams are well-developed, and relativistic field theory is as well. The one topic that I would have liked to see is the LSZ reduction, but perhaps it is not necessary at this level. Overall, this is an excellent self-study or supplementary book for a QFT course. I highly recommend it, with the one caveat below. So, why only 3 stars? I have had the book for two months, used it only at my desk, and pages are starting to fall out! In the past books from Oxford press have been of high quality, both content and printing; so, I am very disappointed. Unfortunately, I have passed the "window of opportunity" to return the book at Amazon. I have included a photo of the book that is starting to fall apart. Note added: I complained to the publisher about the binding problem, and they sent me a hard cover edition, which seems to hold up well so far. The problem appears to be with the paperback binding. Given that, I have upped the stars to 5.

I am about one third through the text. Since I am already familiar with the subject I am jumping around the text. I will update my review later if needed. I thank the authors for providing such an excellent text on Quantum Field Theory. The authors distinguish themselves in this effort in several ways. They continually provide pedagogically sound introductions to the often nebulous concepts of QFT, the prose is well done with the concise examples blended in seamlessly (make sure to read the examples as they appear) and they make effective use of sidebar notes. The text has 50 separate sections. The authors lay out one or two related concepts at time. I find this fine structure is very satisfying. The book stands out in these respects to any other QFT text I have read (in my humble opinion). I think the title undersells the books value. I do think that a gifted amateur may come to understand some profound ideas of modern physics by reading this text. I don't believe this is true of other QFT texts (and it is usually not the goal of such texts). I also should say that I would expect that most of the advanced math will be inaccessible to the amateur. You should go in knowing that. Fortunately the authors have provided the words as well as the math. The problem with the title is that it might prevent an instructor from using it as a course text or as a supplementary text. I hope I can find time to return later and comment on specific sections.

As an "amateur", I find this book pretty hard to study from (which may safely be said on any QFT book) and which has some omissions as for the math. Having said that, I could make some progress with this book and I have general feeling that it teaches the subject in a non-boring, reasonable and intelligent way. The authors definitely put much thought and consideration into it and this book, while teaching the standard topics, follows its original path and style, not repeating any standard textbook on the subject. As another reviewer mentioned, this book fills a gap between level of not knowing any QFT and the level of the standard QFT textbooks and while there is no any significantly better and complete QFT book for this "amateur"/introductory level, I think that having this book in one's library is simply unavoidable either as a main studying text or as a complementary to other books.

I am a retired mathematician and surely I do have the prerequisites fror reding that book as a novel as other authors already wrote ; this book is absolutely fantastic ; this is not to say that there can be no improvement but first of all , I got to underline how outstanding is the writing , the presentation the humor; I cannot stop reading , come back , trying to solve exercises which are in general interesting , adapted ,and the only way to know that you have understood ; I could write pages about my admiration ; the title is a kind of joke but if you are like me and try to understand what's the cathedrals of moderne times are , please read this book, reread , take it with you just in case you get bored somewhere ; this book takes you uphill ; in the worst situations , this book lets you escape from sad thoughts Wonderfull ! Ah , and I forgot : if only maths courses could be tought that way at least in part !!!!The fact that physicists of that rank complain about recrimanations of mathématcians for the lack of rigor is something that SHOULD DISAPPEAR in the years to come ; Mathematics should be made SIMPLE BUT NOT A BIT SIMPLER . These critics seem to me to come from Middle age ! BY learning QFTGA you will also leran a LOT OF VERY GOOD MATHEMATICS and probably make you feel better in learning maths seriously Some critical remarks ; 1) How can you write to the authors, this should be added 2) All of a sudden appear relativity theory ; OK that's mandatory ; some explanations are given ; OK and then comes the problem of spacelike events with ana interesting paragraph about the problem of concilating clasical Quantum mechanics with relativity ; this leads to considérations WHICH ARE INTUITIVE but still unclear to me about commutativity of observables for spacelike events but the worst is to come ; relaitive to that question there is an exercise ............ Well well well ; while it is clear that for spacelike events x and y you can interchange them this is no problem it does NOT clearly imply that the expression for the commutator of the 2 Observables is 0 ; unless you reverse time which of course is also allowed in that case ; wether this is the right explanation is yet unclear to me and this is based on a physical argument not a mathematical one ; by the letter I do not intend to say that you cannot perform the changes as mentioned in the formulaes it just wish to indicate that the physical argument seems to be the only way to get the required conclusion; this is troublesome somehow ; other books spek about special axioms like the wonderfull 'Tourist guide for mathematicians ' from G Folland or "Einstein gravity in a nutshell" of A Zee ( this book derves a special critic ; I saw nowhere something of that kind) where the question is alluded to but for a PROOF , one has still to wait or take it for granted which I dislike...

For a long time I have been trying to self study towards understanding the standard model Lagrangian. Some books I tried were too simple and I did not get much. Others had too much rigor and detail that I gave up. But QFT for the gifted amateur had me hooked from the first two chapters. It moves fast, giving just the right amount of information. And it has hints and exercises if you want to try harder and get a deeper understanding. I am in chapter 10 and still going. Thank you, this is the book I was looking for all these years.

Amateur is a word that should never be used in the same title as QFT. It implies that you can approach the subject with limited background knowledge. That is not the case here, though I can see a need to give it a title that clearly differentiates it from a school textbook. So I want to first address who this book would be best for. A physics or engineering major who has made it through his or her second year of math should have the necessary background, though see below for what exactly that means. What I have found is that if you've taken application-oriented courses on linear algebra and differential equations (With titles like "Applied differential equations" or "Linear algebra for engineers") and third-semester calculus (multivariable) that should cover the absolute requirements. Everything more advanced than that, and the book will clearly tell you what processes you will use, and you should look these up on your own. The authors appear to intend the reader to be someone like that: a student with a solid core background in math and the ability to direct further studies in math as needed. Any knowledge of complex analysis, calculus of variations, modern geometry, and modern algebra will be immensely beneficial. In terms of the physics background, having completed a course in modern physics is enough. You should be very comfortable with special relativity and quantum mechanics, and have an understanding of the basic concepts (though not necessarily the math) of general relativity. QFT is not a trivial subject, it is no exaggeration to say that in any other context this would be PhD student-level stuff. The book is difficult but the authors should be commended for making it as close to first principles as it is possible to be. You will learn things, probably just as much math as physics.