Customer Reviews

Quantum Field Theory of Point Particles and Strings (Frontiers in Physics)

5 star:		(5)
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2 star:		(2)
1 star:		(0)

 

 

This book is readable (you don't have to sit down with paper and pencil and work out a page of calculations to get from one line to the next, for most of the text)and it is clear (concepts are defined and explained). It is not really suitable as a first exposure to QFT for the reader would be better off with some familiarity with Feynman diagrams and relativistic quantum mechanics beforehand. With this background Hatfield's book is very valuable as a source for understanding the meaning behind QFT. Many other field theory texts seem to be concerned with little beyond the motions of handling the mechanical formalism and obtaining quantitative results to problems. This book instead gives the reader insight into field theory, does a good job at giving the big picture and stressing the transition from ordinary QM to the field aspect. Besides this, Hatfield's informal prose makes the book enjoyable to read. It has a fair share of typos throughout but most are quite easy to find. Compared to some of the popular field theory texts out there (P&S, Ryder) this one stands head and shoulders above.

This is not a typical field theory book. From the very beginning the aim is to teach the reader all the concepts and methods which will be useful to learn string theory which form the last third of the book. Excellent examples of this can be found in the chapters on path integral and also in the chapter on Fadeev-Popov method. Almost all calculations are shown in step by step detail and it is very useful for the students who are learning field theory for the first time. The organization of the book is a little different from the usual mold of field theory books, but one can get use to it. One just has to realize that while most of the field theory books on the market (except for Weinberg's 3 volume text and one or two other) aim at teaching how to derive Feynman rules and how to calculate a few processes , this book by Hatfield is trying to take the "field theory book" audiance (who are usually phenomenology oriented) to a different playground "introduction to strings". This is an excellent book and a definite break from the old "B&D book 1 and 2" tradition and I would recommend it to both students and teachers (most of whom are still stuck in the old mode) alike. K. M. Maung Department of Physics Hampton University Hampton, Virginia 23668

I endorse most of what the reviewer below says except that Jasonc65 from Wilmington has forgotten that the derivative with respect to complex z=x+iy is d/dz=1/2(d/dx - i.d/dy) so that he should have got pi=half[i.phi(star)] by both methods - which is the right answer! Hatfield has simply got it wrong. Similarly,pi(star)=minus half(i.phi). For the correct treatment see Franz Gross "Relativistic Q.M. and Field Theory" chapter 7. And it's not the only error; simply "plugging (2.52) into an equation like (2.47)" clearly does not give (2.50) and (2.51) but gives an imaginary probability density and no i-factor in the spatial components.
Hatfield's treatment is not the step by step approach claimed but rather piecemeal and with a cavalier attitude to index house-keeping minus signs and factors of i and 1/2 etc. He is further let down by the typesetting of Perseus books that makes hardly any use of boldface characters, uses a point size for indices and suffixes not much smaller than the normal font and an almost typewriter-like character spacing in equations and formulae that make them sprawl across the page in a way less easy to scan than most other publisher's neatly grouped expressions.
For a step by step introduction that is clear, reasonably rigorous and more readable than Hatfield, I would strongly recommend Lewis Ryder's QFT book notwithstanding that it is mainly oriented towards the path integral formulation.

This book promises to be a nice read for someone with minimal background. And many people with backgrounds in physics say it's an easy read. Maybe it is for them, but not for me. Now, I admit, I am a wannabe physicist. Most of my background is in pure mathematics and computer programming. However, I have recently taken up an interest in physics, and of all the sciences, I find that books in advanced physics are the most difficult to understand, in general. It has taken me many painful hours just to understand the Langrangian and the Hamiltonian, and just last week I finally mastered Noether's theorem. And by page 20 of this book, I'm exposed to the Lagrangian density, kind of a continuous extension of the notion of the Lagrangian. Well, generalizing from finitely many particles to a continuous field is not really that difficult. And I guess that is a very important insight in and of itself. But as I read the next 5 pages, I am absolutely dumbfounded by the stretch of rigor. I can't guess what rule they'll break next, as they assume that every calculation rule will carry over in their transition from one domain to another. In fact, as I write this review, I am still stuck pondering page 25, wondering how they justify every single step.

This is not the first time I've tried to read this book. I've had to frequently consult other books on mathematical physics before I could proceed any further. Now, I admit, that while my background in mathematics is thorough, I've never had a formal education in physics, and I'm trying as best as I can to read all the books on mathematical physics, quantum mechanics, QFT, QED, GR, etc. And I think I have the handle on the Hamiltonian, and how it is used in both classical and quantum mechanics.

On pages 21-22, I have to pour over calucations using integration by parts, and using some unstated boundary conditions, a minor difficulty with which I can cope. But then I find out the the author wants the Lagrangian density to depend on a complex function, and it's conjugate. So while I'm stuck in the middle of page 23, I have to redo all the calculations in my head. Now, that sure isn't step by step detail, as the preface claims. The author doesn't even tell me how I'm supposed to differentiate with respect to the complex functions. Am I supposed to treat the field and its conjugate as complex variables, or am I supposed to pretend that the Lagrangian density really depends on the real and imaginary parts of the field and thus consider two real fields instead of one complex field? I've tried both methods, and neither one of them satisfies my sense of rigor.

In equation (2.52), the author gives the Lagrangian, promising the reader it can easily be calculated by working backwards through the previous equations. I don't find that easy to do in my head at all. I've managed to work forwards and verify that the Lagrangian satisfies the invariance and reproduces Shroedinger's equation. But that was only after I poured over the next paragraph and realized that the transformation factor was supposed to be an imaginary number. Until then, it didn't make sense at all.

Now, I get to (2.53), where Hatfield gives the conjugate momentum as pi = i conjugate phi, without showing any intermediate steps. I tried differentiating with respect to the real and imaginary parts, and I got pi = -i phi. When I tried it again with complex differentiation, which I feel is less plausible, I got pi = i/2 conjugate phi. As always, either I'm not understanding what how the author wants me to make the transition, or else he's doing a sloppy job of it. Of course, like most other physics books, there are arithmetic errors that I have to sort through, and that only makes it worse. I find out only after pondering for days on a single line that the author meant a plus sign where he used a minus.

Well, I tried to forget about this confusion and move on. The author gives the Hamiltonian in (2.55), and then begins to discuss how to second quantize the result. Now, I'm not even sure how the differential operator carries over. In order to justify the claim that (2.55) reproduces the (2.37), it seems that I have to now assume that both d/dx and V(x) commute with phi(x,t). In the first quantized system, this is pure nonsense.

Now, I'm on page 25, where the author is discussing expansion in terms of eigenfunctions. It is smooth sailing until I get to (2.59), where in order to justify the last step, Hatfield makes the absurd claim (2.60), and I'm still trying to figure it out. I can only justify that claim if I confuse integer variables with continuous variables and treat the equation as a matrix equation. After all, you're dealing with a unitary matrix. But just try it with Hermite functions (energy eigenfunctions for the harmonic oscillator problem) and you'll run into problems with infinities. Of course, calculations with the Dirac delta function have never been fully rigorous, so maybe I'm kidding myself.

As you can see, I've only begun the book, so I can't really give a complete review of the whole thing, but it sure seems to be promising to be one headache after another.

This very readable book includes all three representations, operator, path integral, and Schroedinger, and so is unique. There are many original calculations and the author has been thorough, and yet he keeps the reader interested.This is the best book I've seen in QFT for graduate students, people interested in QFT topics and specialists too.

This book is nice to read, I agree with most of the previous reviews about this. Some things are interesting, e.g. the chapter on Schrodinger picture, which is almost completely ignored in most textbooks. The style is very readable and the text gives some useful insights. However, it is not suitable as a reference on QFT or on strings because a number of subjects are left out: renormalisation of gauge theories (only QED is handled), symmetry breaking, the standard model, dimensional regularisation, supersymmetry, superstrings. In less pages, Ryder covers all these subjects, except strings, but in the end gives less insight on the inner working of the theory.

This is a very good and complete book on the subject.
Highly recommended both to learn the subject or as
a reference. It's a few years old now, but very worthwhile.

The last third or so of the book is an introduction to string theory.

This is a very comprehensive and readable book. I especially liked the treatment of path integrals. Definitely one of the best books on QFT in my opinion.

While this book contains some interesting material such as the schrodinger approach to qft, it is not that helpful for learning either field theory or string theory. For one thing, it's not even remotely possible to do justice to both topics in one book, so as a result both are covered too briefly to be really useful.