The structure of the gauge invariant (particle number preserving) C*-algebra
generated by the resolvents of a non-relativistic Bose field is analyzed. It is
shown to form a dense subalgebra of the bounded inverse limit of a system of
approximately finite dimensional C*-algebras. Based on this observation, it is
proven that the closure of the gauge invariant algebra is stable under the
dynamics induced by Hamiltonians involving pair potentials. These facts allow
to proceed to a description of interacting Bosons in terms of C*-dynamical
systems. It is outlined how the present approach leads to simplifications in
the construction of infinite bosonic states and sheds new light on topics in
many body theory.Comment: 36 pages, no figures; v2 - v6: references added, typos and mistakes
corrected; v7: version published in CM
