Quantum Kinematics And Dynamic [Paperback]

Schwinger was arguably one of the four or five brightest physicists of his era in terms of sheer intelligence, and he was also something of an iconoclast. This book beautifully demonstrates both -- it is a highly nontraditional axiomatic development of quantum theory, where the clear expectation is that by developing things extremely clearly from a minimal set of postulates and choices the "right path" on to theoretical breakthroughs becomes clear. I agree completely, although I also believe that some components of that "right path" -- for example, the full richness of Geometric Algebra -- were not yet accessible and need to be mixed into at the right places.

Schwinger begins by developing a priori an algebra of (numerical) measurement in the simplest possible terms. This section has nothing to do with quantum theory per se; rather it applies to any set of quantitative observations of some "system".

He then associates in a very intuitive way the notion that the quantitative measurements obtained in the context of the measurement algebra reflect the state of the system being observed, and works out just how the underlying states can be expressed as a geometry. Some aspects of this geometry are familiar but others are less so. Once again, this chapter is entirely abstract and really has nothing to do with whether the system in question is classical, quantum, or something else entirely. The system is viewed as something that has states, those states form a mixed discrete/continuous geometry, and the states are connected to quantitative measurements via the unknown properties of the measurement process itself. In this chapter he introduces the dirac bra/ket notation as a natural way to express the geometry and its norm/metric (inner product).

Schwinger then posits the fundamental question -- do all possible measurements performed on the system always return the same result independent of the order of measurement, or are there some measurements that will yield different results when performed in different orders? This is presented as an axiomatic choice -- one answer leads of course to classical mechanics, the other to quantum mechanics. Only at this point does the book begin to be explicitly quantum mechanical.

Schwinger then formulates (in not unfamiliar but nevertheless compellingly presented ways) a dynamical principle, identifies classes of non-commuting measurement processes, and derives basic quantum theory from no further assumptions. It is beautifully minimal, and one can clearly see the forks in the road he takes and why one takes the branch he takes at each point.

The rest of the book is a gold mine -- Schwinger tries to tackle many of the most challenging issues of the time he delivered these lectures in novel and unconventional ways. They didn't "work" -- there are no breakthroughs here and history has given us in some cases alternative ways of solving or understanding the problems that are now "accepted" -- but his ideas and approach are wonderful to review, especially when one realizes that there was so much that wasn't known fifty years ago that might well inform new attempts to re-tackle those same old issues, or attempts to make progress in e.g. string theory and unified field theory that utilize his unconventional but very systematic approach.

I routinely use this book to help philosophically-minded students introduce themselves to quantum theory via the first three chapters; some of them go on to puzzle over the latter part of the book (as I still do) to see if there is anything yet to be gleaned from it. The book's lecture note format is particularly well suited to this -- one can read the first part of the book and work through everything in at most six or eight hours, total -- a lot of reward for such a small amount of work!

Feynman once said that "nobody understands quantum mechanics". I think that he was right, but a few people understand it far, far better than others: Dirac, Schwinger, and Feynman himself being luminous examples. Students of quantum theory can do far worse than to avail themselves of the words of these masters, especially when they are so tersely and clearly written.

Julian Schwinger was one of the greatest minds of our century. He learned, as I heard at one of his semminars, quantum mechanics by himself as he was about fourteen from the horse's mouth, that is, the great book of Dirac, "Principles of Quantum Mechanics". One could consider this book as built around Dirac's. It starts by introducing a pre-Dirac notation, symbols which represent measurements. These symbols "factor out" into Dirac's bras and kets when the system is in a pure state. The mathematical properties of these symbols, therefore, follow from the way quantum mechanics describes experiments. The dynamics is introduced through the use of an action principle, soon explicited in terms of continuous transformation groups whose infinitesimal generators include the observables. This action principle turns out to be a differential version of the now popular Feynman action principle, which introduced the concept of path integrals. Schwinger's book is a! barely explored mine of gold. Most of his ideas are there, waiting for you! I think this is the second most beautiful physics book I ever met. The first, of course, is Dirac's. I think Schwinger would agree with me.

› Go to Amazon.com to see both reviews  5.0 out of 5 stars