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.

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 seriouslySome critical remarks ;1) How can you write to the authors, this should be added2) 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.