  Within the C*-algebraic framework of the resolvent algebra for canonical
quantum systems, the structure of oscillating lattice systems with bounded
nearest neighbor interactions is studied in any number of dimensions. The
global dynamics of such systems acts on the resolvent algebra by automorphisms
and there exists a (in any regular representation) weakly dense subalgebra on
which this action is pointwise norm continuous. Based on this observation,
equilibrium (KMS) states as well as ground states are constructed which are
shown to be regular. It is also indicated how to deal with singular
interactions and non-harmonic oscillations.
