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Relativistic Quantum Mechanics (Pure & Applied Physics)

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Forty years latter, Relativistic Quantum Mechanics by Bjorken and Drell remains a classic for all those who want to introduce themselves into the basics of propagator theory. The book does a wonderful job, offering a very intuitive approach to quantum field phenomena, focusing on the applications rather than the formalism. A great choice for a very first text book.

The one thing that is not very pleasant in this McGraw-Hill Science 1998 edition, is that the actual presentation has nothing to do with the image promoted by amazon as the paperback cover, which looks more than the old 1964 one. This customized edition comes in an awful cover that has an squared perforation designed to allow to see the book's name printed on its very first page (there is one more on the back cover for the bar code). A terrible idea to save the work of designing a real cover, to me, deserved for a classic.

The interior is as the College Custom Series products announces, just camera ready copy. No high quality at all.

Ever since I had first started learning about advanced Quantum Mechanics and Quantum Field Theory the classical textbooks by Bjorken and Drell had loomed in the background as referenced by most modern Quantum Field Theory textbooks. I finally had a bit more time this summer to go into some detail in older treatments of relativistic quantum mechanics and field theory, so I decided to pick up this book and go through it. The book turned out to be eminently readable, with a good old-fashioned "Physicist's" way of explaining even the most cumbersome calculations. It serves as an interesting bridge between the historical development of relativistic quantum mechanics (or more accurately, wave mechanics) and quantum field theory. There aren't that many textbooks that give a full treatment of Dirac's equation in the context of hydrogen atom, and from that point of view alone this is a valuable book. The propagator theory is introduced gradually and pedagogically, and in more detail than in most other works these days. However, some of the notation is a bit quaint, although clearly recognizable to the modern readers.

A large part of the book is dedicated to perturbative propagator techniques that are these days a standard parcel of the quantum field theoretical toolkit. Furthermore, most of the old conceptual justification for the internal consistency of the relativistic quantum mechanics (like the hole theory) are no longer viewed as accurate and these thorny issues are best dealt with within the quantum field theory proper.

The last few chapters deal with nuclear reactions. Since the book predates both the Weinberg-Salem model and the QCD, it is not surprising that most of the material from these parts of the book is used much anymore. However, it is still a very important and useful read for anyone who is interested in learning about how the theoretical physicists think, and not just with the final "correct" theories.

This is an old book. About half of its pages are completely out of date ( Fermi's formulation of weak interactions and the no-quark/no-gluon treatment to the strong/nuclear interactions ).

Relativistic Quantum Mechanics was a very advanced subject when the book was wright and you can feel that the book was written for very smart guys.

The style is very concise and fast. There are some typos also.

You should try Walter Greiner's Quantum Electrodynamics and Relativistic Quantum Mechanics books for a gentile and friendly (no-genius) approach to the subject.

... try to find a bunch of used copies. The printing quality (including the cover) is so poor that you will need at least five (unread) copies if you actually intend to read the whole text. I am not joking!

Contentwise - a good RQM book.

A bit old-fashioned, but that seems to be one of its strengths. I feel like no one book does a very good job of describing quantum field theory, but some books do a good job of describing some parts of the subject. And this book does a good job describing propagator methods, or Green's functions, which in other texts seem pulled out of the author's butt.

This book is in many way a very good book. Despite being written 35 years ago, it is still sometimes used in classes. It is perhaps a little terse, but overall is a good introduction to the subject

I used to teach quantum mechanics to chemistry graduate students. With chemists you couldn't go much beyond Schroedinger's equation, H*psi=E*psi, written symbolically as you see it, or they would complain to the chairman. Once a student proposed solving the equation by writing psi = E*psi/H. I was of course outraged, but if you couldn't persuade the students to deal with the operator nature of H, it was a perfectly reasonable idea, giving a statement of a conservative classical Hamiltonian.

Dirac's equation is written in the Schroedinger form using Dirac's definitions for H and psi, which are respectively a 4 x 4 matrix operator for H and a 4-component column vector for psi. But I feel like the student who had not been told - or perhaps did not ask - what H*psi=E*psi really means mathematically and physically. Why? Authors of texts in relativistic quantum mechanics, including this one, do not point out that Dirac's equation can be written in the Schroedinger form only if all four components of the vector wave function oscillate harmonically in time at a single frequency, ome = E/hbar. It's easy to see, Reader. The time-dependent solution is given by Dirac as the product of the harmonic function exp(-i*ome*t) and a column vector containing four time-independent components such that each component of the column vector must be assumed to oscillate in time at the same frequency. Schroedinger himself examined this point in his 1930 paper in which he solved Dirac's equation for a free electron in the time without using Dirac's temporally harmonic solution and found a speed-of-light quiver or tremble motion - Zitterbewegung - with frequency 2mc**2 and amplitude equal to the Compton wave length. Since Dirac's temporally harmonic solution is not the exact solution to his time-dependent equation, I will henceforth call it his harmonic ansatz.

Zitterbewegung, which is predicted by the exact time-dependent solution, shows us that Dirac's time-dependent equation is manifestly inseparable in space and time. Nevertheless Dirac's harmonic ansatz is regarded by the theoretical physics community as giving the only physically interpretable solution of Dirac's equation, which in the authors' words gives enough "truth" that it should not be discarded. Again the authors don't distinguish between the equation itself and the harmonically restrictive solution Dirac used to separate space and time variables, leading to his famous exactly solvable time-independent equation (this analytic solvability of the time-independent equation in the precomputer age makes the harmonic ansatz very appealing), the hydrogen-atom solution, and the propagator formalism which are the fortes of this book. The experiments which can be respectably proposed or performed are only those whose results are interpretable using Dirac's harmonic ansatz. Is nature on a quantum level really harmonic in the time and separable in time and space?

Physicists must obtain "answers," which is a complaint I have heard when I try to interest friends of mine in the points I am raising in this review. So it is not surprising that the authors do not take up these points, but at least a lecture or two could have been devoted to explaining that Dirac's temporal solution is not the exact solution to his time-dependent equation but is rather a solution which leads conveniently to an equation in 3-space which can be solved exactly using standard methods. Dirac, as a skilled mathematician, was able to obtain "answers," but in my view his great contribution is the still unexplored equation itself and not his solution trick, whose result is the subject of this book and of virtually all work thereafter.

Reader, you can easily convince yourself that the harmonic ansatz is equivalent to solving Dirac's coupled first-order time-dependent equations by adiabatic elimination, a procedure widely used in the optical-physics literature to approximately solve temporally coupled equations. Hence Dirac's "truth" is founded on an approximate rather than an exact solution of his time-dependent equation.

What is this "truth" which the authors tell us saves Dirac's equation? Again the authors should have said saves Dirac's temporally harmonic solution to his equation. Like park rangers on government salaries interpreting nature for us, they guide us through a maze of interpretations which must accompany the harmonic solution for it to make sense. The negative energy levels must be filled with electrons to avert the spontaneous radiative collapse of an atom. The reality of a positron amounts to an absent electron in a negative-energy level. A manifestly single-particle theory must have a many-body interpretation for its solutions to make sense. Further mathematical spit and polish - second quantization (presented in their companion volume on relativistic quantum fields) - inspired by particle phenomenology is applied to the harmonic solution to make it give the answers one wants. Mathematical theory must be augmented by physical argument to remove divergences which arise in applications such as the Lamb shift in atomic spectroscopy. In summary the exact time-dependent solution is not interpretable within the framework of acceptable experiments and is therefore rejected as unphysical, even though it is the exact solution. Experiments which are not interpretable within the framework of the harmonic solution are not acceptable, even though the harmonic solution is an approximate solution. Such is the censorship of speech in theoretical physics.