Customer Reviews

Advanced Quantum Mechanics

5 star:		(5)
4 star:		(2)
3 star:		(4)
2 star:		(1)
1 star:		(1)

 

 

This is a very fine book on quantum electrodynamics and should not be confused with Modern Quantum Mechanics, which is a postumous text on quantum mechanics, too formal to my taste. Advanced Quantum Mechanics, on the other hand, is quite the opposite. The treatment of field quantization is very intuitive, based on Fermi's ideas, and Physics is always kept to the forefront. Calculations (there are plenty of them; this is not a couch book) are very detailed and, alas, must be redone with much attention, for typos are quite frequent. I believe this to be still the book to be recommended for a beginner. She should, after all, know the physics, and be able to do a back-of-envelope estimative of the size of Lamb shift, by Bethe's method. The book teaches you that.

Despite the title, the subject is Quantum Electrodynamics, meaning the physics of photons and electrons in interaction. So you'll find Dirac equation, Feynman diagrams, renormalization, Lamb shift, etc. There are hordes of books devoted to that. So what is the difference? The diference is Sakurai. He just couldn't write badly. And here he chose also a very good point of view: avoiding any excess of formalism. The book uses Dirac equations, basic principles of quantum mechanics and relativity, perturbation theory and common sense to derive approximate and accurate descriptions of all phenomena involving photons and electrons, including Lamb shift. You'll learn lots of physics and also Feynman's rules of calculation (the Feynman diagrams). And also a little renormalization. But only a little. Then you could go for the recent tomes of Steven Weinberg on Quantum Field Theory. Farewell!

This book represents to a large degree an approach to quantum field theory that is now viewed as somewhat out of date. Modern textbooks and monographs in quantum field theory emphasize functional methods, the renormalization group, the operator product expansion, and topological field configurations. In addition, this book was published before the advent of the electroweak theory, and so readers will not get an introduction to this theory, nor to quantum chromodynamics, the gauge theory of the strong interactions. The only gauge theory actually treated in the book is quantum electrodynamics, although the author does not exploit the gauge invariance of this theory to its fullest potential in the book.

For those readers who want learn quantum field theory, this book would probably not suffice, due to the above omissions. However, the book might still be used as a reference, and one that, as stated by the author, emphasizes the physics of quantum field theory. Covariant perturbation theory and Feynmam diagrams are given ample treatment. In addition, the author does not hesitate to employ symmetry considerations in the discussion of the transformation properties of the Dirac wave function and the quantized Dirac field. The spin-statistics theorem is not proven, but some plausible arguments as to its validity are given, dealing with the difficulty in constructing a quantum field theory for the electron that does not obey the Pauli exclusion principle. And, as another example of the avoidance of complicated mathematics, the author chooses to discuss the Moller interaction between two electrons using the (noncovariant) Coulomb gauge. In this strategy, the transverse part of the vector potential is treated dynamically, and the electron interaction consists of the interaction of the transverse electromagnetic field with the Dirac current and the instantaneous Coulomb interaction between charge densities. Only the transverse part of the vector potential is quantized, but interestingly, the nonphysical, longitudinal parts cancell out in the calculation of the amplitude. This approach may be distasteful from a modern gauge-invariant point of view, but it does suffice to bring out the physics of the problem, and it does serve to motivate the modern approach to the calculation of the Moller cross-section.

Thus, this might still serve to build insight into the physics of quantum field theory. Too often modern texts emphasize the mathematical formalism, the latter becoming more and more formidable as the years go on. The chapter on covariant perturbation theory is definitely worth some amount of time because of this. The reader can then move on to the magnificent fortresses built by the theoreticians of quantum field theory since this book was published. Quantum field theory is definitely still a very active subject, and there are lots of things in the theory that remain unsolved to this day.

The 1 star is only for the condition of the printed text itself, not for any content in the book.

Addison-Wesley has done a grave injustice to this classic with its latest printing. I ordered it a few weeks ago from Amazon, and what arrived was appalling.

The text is not "clean", it looks as though it was poorly photocopied. Every single arrow indicating spin/helicity directions in the diagrams is not clear, and quite a few don't even show up at all. Sub- and super-scripts are very hard to read in many equations and diagrams, due to the poor print quality of the text. Anyone who has read or seen an earlier printing will be sorely disappointed if they order this text now.

Amazon offered to exchange the book for another copy, which I took them up on, but the replacement was just as bad in print quality. It seems as though this is the fault of the publisher. I tried to reach Addison-Wesley for comment, but my email must not have gotten through. I wish to stress that Amazon was fantastic throughout the entire ordeal, and was consistently helpful, swift, and courteous in their responses.

Overall, it's a great book, but I would highly recommend against buying new. If buying used, make sure to ask any seller to provide high-res pictures of Figure 2-3 on page 51 ( you should see THREE gray arrows for the polarization directions), and of Figure 3-9 on page 164, to see if the gray arrows showing the spin direction of the Lambda particle show up clearly. If they do, buy it! If not, it's a bad print copy, and not worth any amount of money.

--John

I would urge the reader not to dismiss this book too quickly on the basis of its age. This book fills a gap that isn't filled by any other text that I know of: it bridges an undergraduate/beginning grad course in quantum mechanics with a course in quantum field theory. My own experience, which I believe is somewhat typical, was to have a graduate course in quantum theory at the level of Cohen-Tannoudji, followed by a field theory course at the level of Peskin and Schroeder. It seems to me that these levels are separated by a virtual chasm.

I suppose it is natural that as theoretical physics grows, topics once considered crucial fall into the dustbin. Perhaps spending a few weeks studying the single-particle Dirac equation might simply be wasted time when one is eager to move as quickly as possible to the frontier of quantum field theory or string theory or whatnot. But to gain a satisfactory (by my own standards, of course) understanding of Peskin and Schroeder (P&S) level QFT, I needed to spend some time in the chasm. For example:

* Spending time really thinking about the Dirac equation was very helpful. Even though one can motivate quantum fields by resorting to special relativity and the axioms of quantum mechanics, it was very useful to understand in what ways the single-particle Dirac equation (over 60 pages in the book) is still useful, and in what ways it needs to be surplanted. This understanding has been very useful in studying, for example, bound-states and corrections to nuclear transition rates, where computations are nearly impossible using only field-theoretic techniques. It was also helpful in understanding the connection between fermionic field operators and single particle wave functions (which is barely a one-paragraph discussion in P&S).

* An elementary treatment of the quantum theory of radiation was very fun and helpful. I enjoyed working through Rayleigh scattering, spontaneous emission, etc. I feel like I can actually perform calculations along these lines, which I certainly didn't feel after P&S.

* In books like P&S or Ryder, the full machinery of Wick's theorem etc. tends to obscure what is actually happening when one calculates propagators and Feynman rules. Sakurai's treatment in Chapter 4 starts with the canonical formalism and derives cross-sections from scratch. While one loses some of the computational ease of simply starting with Feynman rules, one gains quite a lot. It becomes clear how exactly the propagator captures virtual pair-creation in a covariant manner. It becomes clear exactly why one needs to normal order operators in the Hamiltonian/Lagrangian. It becomes clear how time-ordering and normal-ordering work simultaneously when using Wick's theorem in the Dyson expansion, which is something that confused me in P&S. While path integrals offer the quickest route to calculating propagators and Feynman rules, the long route of deriving the photon propagator in the canonical formalism gave me a better understanding of how various pieces combined to yield a covariant result. And so on.

Like any book, there are some downsides:

* The organization is annoying. For example, Chapter 4, home of the discussion on quantum electrodynamics and field theory, is 120 pages long. It seems as if Sakurai thought for 5 minutes about organizing sections, decided it wasn't worth the effort, and just dumped everything into one chapter. I've been using the book for 2 years now, and I still get lost finding stuff in Chapter 4.

* The book uses a Euclidean metric tensor, so that covariant and contravariant indices are treated identically. Sakurai insists it's silly to not use such a metric, and perhaps one makes fewer computational errors, but virtually nobody uses such a metric any more, and converting back and forth is annoying.

* The book is cavalier about its description of both scattering and the quantum vacuum. I know it's subtle and difficult to discuss asymptotic states in scattering theory, or to discuss the vacuum in an interacting field theory, but you've gotta talk about it. Sorry. You can't just pretend everything is the same as in the free theory. You can't just stick the time-independent free-field creation and annihlation operators between the free-field vacuum and just start computing.

* Being written in 1967, the book doesn't at all serve as a complete text on quantum field theory: among other things, modern renormalization techniques, gauge theories and the standard model, and path integration are missing. But as I said, I think this book does a great job of filling the abovementioned gap, and shouldn't be taken as a stand-alone QFT book.

I think the negatives are more than made up for by one very great virtue of the book: Sakurai will always forego the slicker mathematics or the more general theorem if a gritty calculation makes the physical concepts more apparent. This book may seem old fashioned, but it is truly one of the most useful physics books I've ever studied.

This book certainly isn't for the casual reader, but it is a great book for those who want to learn Advanced quantum mechanics and quantum electrodynamics from a distinguished physicist from a different point of view. Sakurai interjects his own beautifully strange and humourous analogies through out the work, such as comparing the creation, anihilation and number operators to the hindu trinity of Brahma, Siva and Vishnu respectively. Again there are some people who don't get this book, yet there are others who love it.

Most of the graduate students in physics and chemistry here at Cal agree that this book is incomplete and glosses over too much of the details. It's also very annoying to read things like, "Proof: The proof is trivial." Anyone studying from this text will be left with the feeling that something is missing. Personally, I prefer the classic two volume "phonebook of quantum mechanics" by Cohen-Tannoudji et al.

This is a great intro into QED, although I seriously recommend Feynman's little QED book. Renormalization is covered, as is most of Feynman's methods. Overall, I would strongly recommend this to any graduate physics student wanting to learn QED and QM.

This textbook gives a rather formal treatment of quantum mechanics. That is not to say that it is in a theorem-proof format like Neumann, for example, but still I find it lacking actual physical context: the author gives too much emphasis to algebraic derivation as means of explaining basic concepts.

Personally, I find Landau much more enlightening (if, as students often complain, harder to read). I would suggest to use these two books as complementary to each other: Sakurai for its clarity and Landau for its physics.

My other favorite, at a more introductory level, is Shankar, for it is very physical and very easy to read.

This is an essential book for a student making the transition from nonrelativistic quantum mechanics to modern field theory. The only drawback is the archaic notation -- I mean, his gamma matrices are Hermitian. This is deplorable! But considering what's on the market, this is the obvious book to read before jumping into quantum field theory.