  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.
