Physics Science

Richard Feynman was always careful to remind his students that the mathematics and formalism behind quantum theory were more than just recipes, but that they also gave a deep structural understanding of the subject. That philosophy seems to have been the guiding one in the writing of this monograph. The entire monograph is single minded in its devotion to a rigorous development of the algebra behind the theory.

Any good mathematician will cringe when confronted with the appeals to intuition or common sense so frequently used by quantum theory texts to justify the mathematics, and no such appeals are present in Araki’s outstanding monograph. What’s more, the book is as self-contained as one could expect from this kind of monograph, and the notation is modern (so, if reading Wigner or von Neumann has ever caused you a headache, this book might be the remedy).

Even better is Araki’s use of C*-Algebras throughout the text. Often, the use of C*-Algebras is mentioned in the physics literature, but rarely expounded on in an introductory fashion. All too often, we’re left to dig through the journals only to find applications to very specific structures which have been modified, for the sake of mathematics, in such a way as to lose their physicality. Of course, there is nothing wrong with those kinds of studies, but they aren’t physics. Araki’s book is.

The downside is the exorbitant price, and I do not own a copy as a result. It would be worth ensuring that you have access to a library copy, and this could also probably motivate some very thorough note-taking.
Rating: 5 / 5