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Feynman R.P., Hibbs A.R. Quantum Mechanics and Path Integrals

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Feynman R.P., Hibbs A.R. Quantum Mechanics and Path Integrals
McGraw-Hill Companies, 1965. — 365 p. — Series: International Earth & Planetary Sciences
ISBN-10: 0070206503 ISBN-13: 978-0070206502
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!
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