Customer Reviews

Quantum Mechanics and Path Integrals

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This is a book every physicist, or student of physics, should study. Here the author describes the principle of action in quantum physics. It is not a minimum action principle, like in classical mechanics: you can, however, derive the classical minimum principle from it, in the classical limit. Why is this important? Well, it so happens that the famous gauge field theories could only be quantized under this formalism. Feynman, of course, reformulates everything with his technique, so that the book is very enlightening: it is a rich experience to see well-known things under a different viewpoint. But there are many new things also. The applications are brilliant, covering just about everything: electrodynamics, statistical mechanics, you name it. A new mathematics is introduced by Feynman, a theory of integration in a space whose elements are curves (path integrals). As far as I know, the rigorous theory of this integration does not exist as of now. Undauntedly, Feynman is able to guide us to very important results by using intuitive methods, and checking the validity of a result by obtaining it by two different ways, for instance. Don't miss, by the way, his discussion on the role of rigor (in the mathematical sense) in physics. There is a section on that!

The path integral technique of quantum physics is used in nearly all of modern physics, ranging from astrophysics to condensed matter theory. In this book, the author and developer of path integrals, R.P.Feynman, provides us with a unique insight into this theory and its applications in the various fields of physics.
The first few chapters present Feynman's view on the fundamental concepts underlying quantum mechanics. From this intuitive view, path integrals are introduced. Later chapters cover more advanced topics like the perturbation method, quantum electrodynamics and the relation of path integrals to statistical mechanics.

Most books on quantum mechanics tend to drown the underlying physics in a sea of mathematics. Feynman however, presents his celebrated theory in a clear, concise way, keeping the perfect balance between mathematics and physical insight. Definitely a book anyone interested in quantum physics should keep under his or her pillow !

This is an extraordinary book, a great example of Feynman's intense originality. Of course he put quantum mechanics upside down, with his path integrals (you DERIVE Schroedinger's equation!), and this is extremely enlightening. But that is not the whole story. The book is full of profound insight on practically anything, even elementary matters, such as the consideration of continuous spectra and the role of mathematics in physics. The idea of summing over histories propagates from quantum dynamics to everything in sight, leaving no stone unturned. One of the most important books on science, ever. Very readable!

Written in the typical, beautiful Feynman style, this book is fine for an advanced student who already knows quantum mechanics and Green functions from a standard source like Sakurai or Merzbacher. It presents Feynman's interpretation of quantum mechanics in chapter 1 via the two-slit experiment, and the rest of the book is devoted to showing how to formulate and calculate the one particle Green function for simple systems, systems with completely integrable classical analogs (it's implicitly assumed that Ldt is a closed differential, where L is the classical Lagrangian). The path integral formulation was also later used by other researchers to arrive at a semi-classical approximation to the three body problem, a nonintegrable and even chaotic classical system (nonintegrable classical systems cannot be solved by the standard method of finding a complete set of commuting constants of the motion).

The functional integral formulation of Brownian motion was formulated earlier by Norbert Wiener. An analogous formulation of quantum theory was arrived at independently by Feynman, who took seriously a conjecture by Dirac about the meaning of the exponential of the classical action as a probability amplitude. A more complete treatment of classical Brownian motion (including the so-called 'Feynman-Kac formula' for Brownian motion) was given later by Mark Kac in "Probability and Related Methods in the Physical Sciences".

Chapter one presents with Feynman's interpretation of quantum mechanics, the interpretation accepted by theorists today, as nonclassical rules for combining probability amplitudes for particle propagation. Waves are not mentioned because the mental gyrations inherent in the Copenhagen 'wave-particle duality' are completely avoided in the Dirac-Feynman approach. See, as forerunner of Feynman's interpretation, Dirac's discussion of photons interfering with themselves in a hypothetical two-slit experiment, in the introduction to his famous text "Quantum Mechanics".

In other words, this book is for students who are ready to face the fact that there is no 'wave-particle' picture, or any geometrical picture of reality, at the quantum level: the reader who really understands Feynman's description of the two-slit experiment will realize that we cannot say about the hydrogen atom that an electron is moving about the nucleus, unless we do a scattering experiment to detect the electron (an electron doesn't follow a path, nor is it in two different places at the same time, there is in the end only the space-time propagation of quantized fields). As Feynman admitted, we do not really 'understand' quantum mechanics, although we can do all of the calculations describing experiments. The 'measurement problem', the Einstein-Podolsky-Rosen paper and subsequent experiments and papers on quantum teleportation make this viewpoint clear. Quantum mechanics, nature at the microscopic level, is stranger than anything that you can imagine!

The Dirac-Feynman interpretation of quantum theory is presented by Sakurai, who also discusses the measurement problem. Merzbacher doesn't teach Dirac-Feynman but does discuss Galilean invariance via gauge transformations, and sets up the two-body problem in a form that is useful for understanding the enstein-Podolsky-Rosen paper.

This is a prety good book. Too bad people are selling the damn thing in the 400-1600 dollar price range. Mc-Graw Hill needs to get someone to fix all the typos (oh, and there are a ton of them) and then re-print this book so I don't have to spend a thousand dollars on a copy.
The Path Integral approach to Quantum Mechanics is pretty snazzy, and it's neat to see how Feynman comes up with the Schrodinger equation, and the commutation relations, and all that via the path integral method.
Also, the book does a good job of explaining scattering, and perturbation theory, which seem to be a little more natural with Feynman's approach to quantum mechanics.

P.S. The reviewer *below* refers in his review to the "...reviewer above." But, *I* am the "reviewer above" even though I am not the person to whom he is referring. The reviewer *below* is obviously an idiot.

There is an emended version due out soon with Daniel Styer! The price will be under $20 and many of the mistakes will be corrected.

This is a great book to learn path integrals from if you are just getting started in field theory and want a good physical feel for them. It is too bad there aren't copies available for a reasonable price. $500 is just too high a price to pay.

See your way through an astounding tour of how nature works. As a physics student or professional your education is incomplete without studying this book.

Be sure to get the full ERRATA for the text from me (write mathematicus at yahoo). BTW the book is expensive because it went out of print in 2001. I've been badgering the Dover editor to reprint it for years, but no dice!

As far as I can tell, every other discussion of the subject of the path integral formulation of quantum mechanics is just a poor copy of this book. No one can match it for how simply, yet clearly the topics are explained. It does, however, have a number of typos (though I was lucky in that the previous owner of my copy had gone to the trouble of fixing them with a felt pen).

This is an outstanding book for those who seek i) an intuitive understanding of quantum mechanics (QM) and quantum electrodynamics (QED); or ii) a guide on the Feynman path integral method. Within either of these contexts, the text and derivations are crystal clear and highly pedagogic.

If what you are looking for is a complete, thorough course on QM or QED, this book should not be taken as a standalone text. It has to be used in conjunction with another appropriate textbook. For example, I use this book together with Rodberg and Thaler's book on quantum scattering theory for both research and teaching on scattering theory. Other textbooks would be applicable to other purposes.