Reviewed in the United States on June 13, 2016
This book is unphysical. What do I mean by that? Let me give a few examples:

1) It violates causality.

In most models of the universe, effects cannot precede their causes, and events from the future do not influence events of the past. Not so in this book! Arguments tend to follow highly non-classical trajectories, being spread across many different chapters in a topologically non-trivial manner. Admittedly, in a path integral approach to pedagogy, I'm sure you could recover the argument by reading all passages of the book in all possible orderings and averaging by the effective action of the argument. So when an explanation given in this book concludes "the full proof will be provided in chapter 14", presumably there exists a massive phase cancellation of all the material in between, such that all of the intermediary arguments are precisely cancelled by contradictory statements, and the full logic emerges as a continuum limit. However, since pedagogical path integrals are computationally intractable, the only way to evaluate them is by Monte Carlo sampling---reading sections of the text in random intervals and looking for a statistical convergence of reason. I did precisely this, and after convergence the only statements that did not cancel exponentially were the footnotes saying "See Weinberg for details".

On a side note, the well-mixedness of this book shows that it has very high entropy. Thus, by standard thermodynamical arguments, the amount of useful work that can be derived from it is very small.

Of course, this does not prove that the book violates causality---only that it must violate causality if it is to make any sense at all. The proof that it does violate causality will be presented in point (3), below.

2) The notation is not an eigenstate of the Hamiltonian

It is well established that the notation and terminology of QFT is massive. However, it appears that the author of this text has elected to use parity eigenstates of notation, which in the presence of a mass term are no longer eigenstates of the entire Hamiltonian. Thus, the text exhibits flavor oscillations of notation, with e.g. upper indices rotating into lower indices on a periodicity of about 2 pages. This is unobservable for Euclidean field theories, where no experiment can measure the sign of a index, but in Minkowski space it causes the vacuum to become unstable: Plus signs can spontaneously decay into minus signs, resulting in non-local perturbations to the state of confusion, and what mathematicians call a "catastrophe".

3) The logic can be off-shell.

The introduction to this text advertises "mathematical rigor". However, it fails to mention that this rigor is of a very peculiar sort that requires the propagation of non-physical "ghost logic" that is not quantized in integer units of trueness. Admittedly this is very useful for QFT, as it allows one to make fully rigorous arguments using advanced techniques like "proof by assumption", "proof by assertion", "proof by failure to find a counter-argument", "proof by guessing", and "proof by citing Weinberg". In all these cases, one postulates the existence of a mathematical structure which trivializes the action of the details of a theory, propagates the logic (in an unphysical, off-shell way) to a state which is known (or will be shown in a future chapter) to be consistent with experiment, and then shows that since no experiment can distinguish this theory from reality, it must be unphysical. Since it is unphysical, no experiment can distinguish a bogus argument in this theory from a non-bogus argument, and thus we may make all the bogus arguments we want with no energy cost, and as long as the net bogus is exactly zero, it must be gauge-equivalent to a valid argument with the same result. This "advanced" argument may sound like circular reasoning, since moving forwards in time we do not know that the mathematical details are true until they are known to be true, but it is preferable to think about it (in a Feynman-Stuckelberg interpretation) as a retarded anti-argument travelling backwards in time. (By the way, recall that statement about causality that I mentioned above without proving? This provides the promised proof!) If you find this confusing, try to find a counter-example, and convince yourself that it's impossible to argue with this logic.

4) The explanations are non-perturbative.

If you take the off-shell logicons for granted, the arguments presented in this text are perfectly plausible. For example, the occasional trick "guess the solution and check that it's consistent to first order" works very well in all the cases considered in the book. However, if you try to perturb such reasoning, you find that it almost immediately fails (for example, in some of the exercises). This strong coupling is presumably due to renormalization of higher order non-causal proof loops: if you naively try to integrate a non-causal, off-shell logicon into your own argument, you will find that there is a diverging quantum of strangeness to the logic. Since all eigenstates with non-zero strangeness are at best metastable, in order to have your argument not decay long before you finish your proof, you must introduce an ultraviolate cutoff on how hard you think about any arguments presented in this text. This is physically justified by the fact that the microscopic details of the logic consists of (something gauge-equivalent to) a bunch of bogusons and anti-bogusons anyway, which are clearly unphysical. Since we don't understand the microscopic details, we must integrate out the detailed logic, resulting in the observed strong coupling of the text's arguments. Consequently, the only way to proceed in general is again with non-perturbative approaches, summing the contributions of all possible instantons, insistantons, incessantons, cessantons, carryons, tackons, walkons, neurons, rambleons, rambleons, rambleons, and (of course) all possible reasons. After carrying out the computations, I was left with a remarkably elegant solution: See Weinberg for details.

OK, seriously now: My background with this book was in the context of a standard graduate QFT sequence at a top U.S. physics research university. The first quarter of the sequence was based entirely on Schwartz and successive quarters were based on a mix of Schwartz, Peskin & Schroeder, and a little Weinberg. This was the first year Schwartz was used here. My conclusion is that Schwartz is the worst book to learn from of the bunch. Since this review is at variance with many other reviews here, I will conjecture that the root of the disagreement is that the other reviewers seem to have been already well familiar with QFT before picking up Schwartz---I was not. Indeed, I think Schwartz probably provides a valuable fresh perspective on QFT for those who are already old hands at the subject, but it is not so useful as an introduction to the subject. The essential issue may be the text's sloppiness, examples of which are contained in my 4 points above. E.g. the indices (point 2) really do fly around all over the place, which I think most practitioners of this field would agree is poor practice. Of course, this on its own wouldn't spoil the book. A more authoritative criticism came from the instructors I had: During the classes I took, both a TA and a professor separately made statements to the effect "Yeah, Schwartz doesn't tell you everything you need to know." It was recommended to me on several points that I supplement the presentation of Schwartz with that of Peskin & Schroeder or Weinberg. For a beginning student, that completely defeats the purpose of using Schwartz in the first place. And after reading those supplements, I agree that the treatment of other texts is superior.

Schwartz does have some valuable additions to the QFT textbook arsenal---a prime example being his inclusion of spinor helicity formalism---but this doesn't make up for the pedagogical faults. So summarily: If your only interest is to get a hand-wavy, whirlwind tour of modern QFT, this book may do you good. If you are a lecturer looking for new ways to present the subject, this book may do you good. If you are a student trying to learn QFT for the first time, forget this book---go with Peskin & Schroeder or (preferably) Weinberg. MOST IMPORTANTLY: IF YOU ARE A PROFESSOR LOOKING FOR A TEXTBOOK FOR YOUR QFT COURSE, DO NOT USE SCHWARTZ. Another reviewer has called this book the "new standard". It is not. Peskin & Schroeder (despite its imperfections) or Weinberg are still the standards.