- Paperback: 336 pages
- Publisher: Addison-Wesley; 1 edition (January 11, 1967)
- Language: English
- ISBN-10: 0201067102
- ISBN-13: 978-0201067101
- Product Dimensions: 6.2 x 0.8 x 9 inches
- Shipping Weight: 1.5 pounds
- Average Customer Review: 16 customer reviews
- Amazon Best Sellers Rank: #1,408,763 in Books (See Top 100 in Books)
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Advanced Quantum Mechanics 1st Edition
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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.
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.
This is a great intro into QED, although I seriously recommend Feynman's little QED book (for the errors). 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.