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In this article we show that the main C*-algebras describing the canonicalcommutation relations of quantum physics, i.e., the Weyl and resolventalgebras, are in the class of F{\o}lner C*-algebras, a class of C*-algebrasadmitting a kind of finite approximations of F{\o}lner type. In particular, weshow that the tracial states of the resolvent algebra are uniform locallyfinite dimensional.

A note on commutation relations and finite dimensional approximations