A note on commutation relations and finite dimensional approximations

TL;DR

This paper demonstrates that key C*-algebras related to quantum physics' canonical commutation relations are F{46}lner C*-algebras, allowing finite approximations and revealing properties of their tracial states.

Contribution

It establishes that Weyl and resolvent algebras are F{46}lner C*-algebras and shows their tracial states are uniform locally finite dimensional.

Findings

Weyl and resolvent algebras are F{46}lner C*-algebras.

Tracial states of the resolvent algebra are uniform locally finite dimensional.

Finite approximations of these algebras are possible via F{46}lner techniques.

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 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.