I am studying the theory of $C^*$-algebras, von Neumann algebras and unbounded operators in courses on Functional Analysis and Opertor Algebras. Now I want to apply this knowledge to (algebraic) quantum mechanics. I heard that one can "affiliate" unbounded operators to $C^*$-algebras and von Neumann algebras of special types. In particular, many operators in quantum mechanics are unbounded and many authors use the $C^*$-algebraic description of quantum mechanics. How can i connect now unbounded operators to $C^*$-algebras in the context of quantum mechanics? Are there good books where I can study this? Is is possible to describe quantum mechanics with affiliated $C^*$-algebras? Another approach to describe quantum mechanics is via the Weyl-$C^*$-algebra, the $CCR$ and $CAR$ relations and Fock spaces. I know the book from Bratteli about this, but are there also other good book about this topic? Can one connect this two approches of quantum mechanics with each other?
Thank you very much about hints, links and answers on this question.