2
$\begingroup$

I am familiar with quantum mechanics and quantum information at the level of Sakurai and Preskill's lecture notes / Nielsen and Chuang. I want to study the $C^*$ algebraic formulation of quantum mechanics. Are there any good books on that? Mathematical rigour is not a problem, I am willing to push through it.

$\endgroup$

1 Answer 1

1
$\begingroup$

I can recommend "Araki: Mathematical Theory of Quantum Fields." The first two chapters describe an algebraic formulation of quantum mechanics (and can be read without knowledge of quantum field theory). The book begins with an outline/motivation of how an algebraic formulation of a quantum theory should look like, and then presents the mathematical theory in the second chapter. In my opinion, this text is the best compromise between a physical motivated and a rigorous mathematical presentation. In this book you find everything typically needed when working with an algebraic formulation of quantum mechanics including states and representations of a $C^*$-algebra, the GNS construction, symmetries from an algebraic point of view, etc. As prerequisites, you should know the standard quantum mechanical formulation and some functional analysis, but the book also has an appendix summarising the most important results from functional analysis required for the book.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.