A note on commutation relations and finite dimensional approximations
arXiv:2111.15221 · doi:10.1016/j.exmath.2022.08.004
Abstract
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 Følner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of Følner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional.
arXiv comment11 pages, minor revision, accepted for publication in Expo. Math
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