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Deep Beauty: Understanding the Quantum World Through Mathematical Innovation

Hans Halvorson, editor
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Ana Momidic-Reyna
, on

The editor of Deep Beauty: Understanding the Quantum World Through Mathematical Innovations claims that the articles collected in it are intended for those with previous technical trainings in the areas of quantum theory, n-categories in physics, topos theory, bohrification, etc. In fact, the chapters are technically demanding, and most readers will need much time, patience and persistence to profit from them. Even after investing that effort, it is likely that there will still be parts that will leave the reader puzzled or confused.

Nevertheless, this is a very good book, in which some of the greatest mathematicians, mathematical physicists, theoretical physicists, and philosophers have written to help us understand the conceptual foundations of quantum theory. The table of contents will demonstrate the variety and reach of the book. Most readers will find at least one chapter that they can enjoy and understand.

A native of Macedonia, Ana Momidic-Reyna has an M.S. in Mathematics and has also worked for the high energy physicists at Fermilab. While waiting for the opportunity to work on her Ph.D. in mathematics, she keeps up with the field by reading as many mathematics books as she can.

Part I. Beyond the Hilbert Space Formalism: Category Theory
1. A prehistory of n-categorical physics John C. Baez and Aaron Lauda
2. A universe of processes and some of its guises Bob Coecke
3. Topos methods in the foundations of physics Chris J. Isham
4. The physical interpretation of daseinisation Andreas Döring
5. Classical and quantum observables Hans F. de Groote
6. Bohrification Chris Heunen, Nicolaas P. Landsman and Bas Spitters

Part II. Beyond the Hilbert Space Formalism: Operator Algebras
7. Yet more ado about nothing: the remarkable relativistic vacuum state Stephen J. Summers
8. Einstein meets von Neumann: locality and operational independence in algebraic quantum field theory Miklós Rédei

Part III. Behind the Hilbert Space Formalism
9. Quantum theory and beyond: is entanglement special? Borivoje Dakić and Časlav Brukner
10. Is Von Neumann's 'no hidden variables' proof silly? Jeffrey Bub
11. Foliable operational structures for general probabilistic theories Lucien Hardy
12. The strong free will theorem John H. Conway and Simon Kochen.