Fundamental Mathematical Structures of Quantum Theory

Moretti's text is a fun and insightful tour through analytic aspects of quantum mechanics. In particular, it is an excellent resource for the spectral theory of unbounded operators. The text also gives a well motivated introduction into operator algebras, more specifically, C* and von Neumann algebras. 

 

The text under review grew out of notes for a Master's level course at Trento, which itself was an expansion of a mini-course. For this reviewer, the text reflects this lineage: it is not exhaustive and neither a stand-alone text on spectral theory nor quantum mechanics. The text is a collection of fundamental results, examples, and their historical context.  The text could work well for a course when supplemented by Moretti's more expansive Spectral Theory and Quantum Mechanics. 

 

 

This reviewer would find the text most useful as a supplement to a second course in functional analysis based on any of the more classic graduate texts. It is also well suited to self-study by graduate students/researchers transitioning to mathematical physics.

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Ryan Grady is an associate professor of mathematics at Montana State University.