LAUSR

Quantum Measurement. The four authors, one from the UK and three from Finland, do an admirable job of summarising the mathematical prerequisites (of which there are many) of a quantum theory of measurement, and expound various foundational topics ‘from a measurement-theoretic perspective’, systematically presenting the mathematical tools needed to navigate the Hilbert space and other spaces beyond. I must admit that I found it fairly hard going. It’s a challenging read if you are a physicist and not a mathematician. The book is constructed as a series of theorems, proofs, propositions, lemmas and corollaries, with only the very occasional example or figure to motivate the reader. In the second half, it does lighten up a bit and there are some very good short chapters that tackle particular specialised topics. Each chapter throughout the book is supplemented by a detailed set of references for further reading. Consequently, this monograph will be very useful as a reference work. At the end of the day, this is a volume that is really intended for mathematicians. If you like your Banach algebras, are familiar with the Fréchet-Riesz theorem of bounded linear operators, and if you know what a semi-spectral function is, then this book might be just up your street. I suspect that this is probably not an accurate characterisation of most readers of Contemporary Physics, even of those that have an interest in the foundations of quantum theory.