Cluster Expansions in Many-Fermion Theory. II. Rearrangements of Primitive Decomposition Equations

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Abstract
The ``factor‐cluster'' formalisms introduced in the preceding paper are used as a tool for a further development of the cluster theories proposed by Iwamoto and Yamada and by Aviles, Hartogh, and Tolhoek. The primitive decomposition characterizing each of the older formalisms is rearranged into the exponential of a series with a uniform N dependence in the limit of large N. In addition a ``linked cluster'' theorem is proven for the series comprising the exponent in the Iwamoto‐Yamada formalism. Our derivations, unlike those of earlier authors, are valid for all N.