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.