A note on commutation relations and finite dimensional approximations Articles uri icon

publication date

  • December 2022

start page

  • 947

end page

  • 960

issue

  • 4

volume

  • 40

International Standard Serial Number (ISSN)

  • 0723-0869

Electronic International Standard Serial Number (EISSN)

  • 1878-0792

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.

subjects

  • Mathematics

keywords

  • canonical commutation relations; c*-algebras; følner approximations; amenable traces