Cluster Expansions and the Unitary Group

A further discussion of the possibility of product generators (see Paper II) is undertaken herein. In addition it is shown that the unitary group decomposes in a physically plausible way such that the cluster structure appears quite naturally. Through the use of this decomposition it is shown that there are three contributing effects which determine a cluster function: form, dynamics, and background. These three effects are then discussed in the context of the problem of the transferability of cluster functions.