  The standard C*-algebraic version of the algebra of canonical commutation
relations, the Weyl algebra, frequently causes difficulties in applications
since it neither admits the formulation of physically interesting dynamical
laws nor does it incorporate pertinent physical observables such as (bounded
functions of) the Hamiltonian. Here a novel C*-algebra of the canonical
commutation relations is presented which does not suffer from such problems. It
is based on the resolvents of the canonical operators and their algebraic
relations. The resulting C*-algebra, the resolvent algebra, is shown to have
many desirable analytic properties and the regularity structure of its
representations is surprisingly simple. Moreover, the resolvent algebra is a
convenient framework for applications to interacting and to constrained quantum
systems, as we demonstrate by several examples.
