An Introduction To Quantum Field Theory

The best QFT text for intro level

Peskin and Schroeder's book seems to be the standard text for courses in quantum field theory these days. Although somewhat intimidating for the novice, the reader seasoned by reading a good portion of Ryder's book Quantum Field Theory will find himself fairly comfortable. The advantages of the compact (1, sigma) notation used by the authors for Dirac spinors and gamma matrices, although not as immediately transparent as the expressions favored by Ryder, soon become familiar. The use of a more compact notion gives more space for narrative exposition.One discussion that I found particularly helpful in P&S is the explanation for the sign of time dependence for the field operator psi(x) on p.54 using equations (3.91) and (3.92). Because psi(x) is an operator and not a simple wave function, we have to switch to the Heisenberg picture in order for it to have time dependence. In the Heisenberg picture the annihilation operator has time dependence a(p)exp(-iE(p)t). It is then clear that the annihilation side of psi(x) must be proportional to a(p)exp(-p.x), since p.x=(Et-P.r) using Ryder's choice of metric and space time coordinates (with P as the three momentum, r as the three position [x,y,z], and E as the energy). Perhaps this seems like a minor point, but the choice of sign for the exponential in a(p)exp(-p.x) seemed to me to be purely arbitrary before reading this section in P&S.As you might expect, however, some points that should either be given greater emphasis--or explained in more detail are sometimes glossed over. Happily, a good supplement for this text exists in the lecture notes of Cambridge University's David Tong. Tong's notes provide a better understanding of the ideas behind the rotation of the contour slightly away from the real axis (p.95) in order to insure that the integral for the propagator converges. Tong also adds to the authors' discussion of normal ordering and Wick's Theorem.Peskin and Schroeder also provide a very readable discussion of the Higg's model in Chapter 20. Reading this chapter has given me the best appreciation for QFT that I have gleaned thus far.

Peskin and Schroeder's textbook is the standard textbook for quantum field theory courses for a reason. Although it may be a little intimidating for beginners, it covers an almost unmatched breadth and depth of material extremely well, and also teaches actual calculation very well.

Sidney Coleman says this: “…a notorious reputation for difficulty.” (1975 Lecture One of Quantum Field Theory). Peskin and Schroeder say this: “We feel that students who want to become experts in elementary-particle theory and to fully understand its unified view of the fundamental interactions should master every topic in this book.” (preface). If you do not desire to “become an expert” or “master every topic,” turn to another resource ! However, there is more to this book than just that (of becoming an expert). Read: “As we expose more applications of the (Feynman) diagrams they begin to take on a life and significance of their own….we hope that this book will enable you (the reader) to take up this tool and apply it in novel and enlightening ways.” (page 12). That is the reason for studying this book, or, at least the reason I study this book. It is a challenging text, as it should be (being a graduate-level text). My limited outlook:(1) You wait until chapter four for Feynman diagrams, everything else (up to page 77) is merely warming-up. Glance at the exercises in the initial three chapters. An introduction to supersymmetry (problem #3.5, “linking fermions and bosons.”). That exercise utilizes Grassmann numbers (introduced earlier, exercise #3.4, pages 73-74). A clue: exercises introduce auxiliary material and they are somewhat interdependent. At least, read every exercise in order, one after the other and attempt to solve each of them. Problem #4.3 (page 127) introduces linear sigma-model, a model discussed in detail later (chapter 11, page 349). The book has a linear structure.(2) Another pedagogic strategy: introducing a topic heuristically, presenting a detailed examination of the topic later. For instance, chapter four (page 80) will utilize dimensional analysis to “throw out nearly all candidate interactions,” this precedes a detailed discussion of renormalization (chapter ten). Read: “it can be shown that, however complicated a fundamental theory appears at very- high energies, the low-energy approximation to this theory that we see in experiments should be a renormalizable quantum field theory (page 81). A discussion, “guessing the magnitude of the top-Quark width,” (page 747) then follows.(3) If you have not learned by now that analogy is an important pedagogic device, then you will not appreciate Peskin and Schroeder. Analogy is oft-utilized. Examples abound: “by analogy we can construct a similar quantity” (page 365, to statistical mechanics), neutrino cross-section (page 560, analogous to electron-proton scattering), two-dimensional axial current has analogues in four-dimensions (page 659), working out the analogue to electron-splitting for photon-splitting (page 584), the list of “analogies” continues unabated (note the table on page 367, magnetic system).(4) Mathematics kept straightforward: details regards dimensional regularization (page 249) as forthright as possible; then you are asked to assist in those calculations ( “you can easily verify the more general integration formulae.” ). If you are unable to verify those integration formulae, you are lost (page 251) !(5) Functional methods, delightful. Read: “we consider that the Lagrangian to be the most fundamental specification of quantum field theory.” (chapter nine, page 283). Learn of Faddeev-Popov (“isolate the interesting part”) then you churn out the photon propagator (page 297). Read: “the functional integral formalism makes the symmetries of the problem manifest.” (page 306). You get the chance to use the product expansion for hyperbolic-sine in problem #9.2, a five-part exercise. There are other instances to learn of interesting mathematics (the integral, page 262).(6) Read: “this book is primarily a textbook of theoretical methods rather than a review and interpretation of experimental data.” (page 545). That statement precedes an introductory chapter of quantum chromodynamics. This superb chapter seventeen sets the scene (via asymptotic freedom) as preparation for the following chapter (details via renormalization and scaling laws). The conclusion here: “it is remarkable that these simple considerations have led to a description of the strong interactions that is quantitatively correct for a broad range of phenomena…” (page 594).(7) Footnotes are invaluable, sometimes expanding upon a qualitative discussion. For example: a paper by Coleman and Gross (1973, Physical Review Letters) expands upon the discussion of page 543: “among renormalizable quantum field theories in four space-time dimensions, only the non-Abelian gauge theories are asymptotically free.” (Section # 16.7, pages 541-543, presenting the qualitative survey). Another footnote, another paper: “for every spontaneously broken continuous symmetry, the theory must contain a massless particle.“ (1962, Goldstone, Salam, Weinberg). Now, if you do not care for journal literature for elaboration, Peskin and Schroeder will prove less fulfilling because of that !(8) No textbook is perfect, there are shortcomings: You do not find cluster decomposition (chapter four of Weinberg). We are informed that “we have avoided giving a careful treatment of the energy-momentum tensor of a quantum field theory.” (page 682). We are informed that “we will not discuss canonical quantization of the electromagnetic field at all in this book.” (page 79; see Mandl and Shaw for that).(9) Coming in at 850 pages, there is a surfeit of material. The authors have provided more on their webpage: expanding section # 10.5, supplemental material for chapters 13, 16, 19 and 20. More from the authors, too, regards 'Jets' (arXiv 1101.2414).(10) I am convinced that quantum field theory should be developed through multiple volumes (thus, my preference for Steven Weinberg). In a single-volume text, too much material can prove daunting. It is easy to see where Peskin and Schroeder can be overwhelming. In reality, no single resource is sufficient for everlasting comprehension.(11) Conclusion: I can only offer a personal opinion (not teaching from the book nor having taken a course based on the book). This is a graduate level text and there is no reason to include every step of every derivation. If you are not used to “filling in the steps” by the time you reach graduate-level, that is an issue for which Peskin and Schroeder are not responsible (they are explicit regards prerequisites). I like this textbook quite a bit, although my favorite remains Steven Weinberg. I have studied from many texts (30 of them) at one time or another (books published from from 1959 to 2017). If you do not appreciate Peskin and Schroeder there are many options from which to choose (Coleman, Srednicki, Duncan and, of course, Weinberg).

I give this book 5 stars only because it is the best book available if you want to study the real thing in QFT. It is so much more readable than its predecessors it's amazing. That being said you must be ready for this book by having studied quantum mechanics at the level of Sakurai and you probably need to frequently revisit it.You must read this book with pencil and paper in hand to get anything out of it. Sometimes a line or two in Peskin is three or four pages of manipulation. You have to work it out to learn the math skills to absorb the material. QFT is not a spectator sport.Zee's book is a good introduction, I wished I had read it first but for the real thing in QFT you will need this book.

First, this book includes a lot of material and that is why it is considered as textbook for QFT courses in most universities worldwide.Second, these authors makes a pretty good job introducing topics slowly and in a right sequence. I have heard that studentssay that this book is hard... Of course this book is hard!!! But if you have already taken one or two courses of QFT, you will be ableto go through this book without much suffering. I strongly recommend you this book.

Very happy to have this well written source from such an expert in the field.

Our friend's son requested this text by name. He was very happy to receive it!