# Quantum Systems and Resolvent Algebras

June 04, 2013

This survey article is concerned with the modeling of the kinematical
structure of quantum systems in an algebraic framework which eliminates certain
conceptual and computational difficulties of the conventional approaches.
Relying on the Heisenberg picture it is based on the resolvents of the basic
canonically conjugate operators and covers finite and infinite quantum systems.
The resulting C*-algebras, the resolvent algebras, have many desirable
properties. On one hand they encode specific information about the dimension of
the respective quantum system and have the mathematically comfortable feature
of being nuclear, and for finite dimensional systems they are even postliminal.
This comes along with a surprisingly simple structure of their representations.
On the other hand, they are a convenient framework for the study of interacting
as well as constrained quantum systems since they allow the direct application
of C*-algebraic methods which often simplify the analysis. Some pertinent facts
are illustrated by instructive examples.

Keywords:

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