In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of F{ \o}lner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of F{ \o}lner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional.
Categories: math.OA math-ph math.MP