Cluster Expansions in Many-Fermion Theory. I. ``Factor-Cluster'' Formalisms

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Abstract
Cluster development may furnish a powerful device for the calculation of the expectation values of the observables of a many‐fermion system with respect to dynamically correlated state vectors. The generalized normalization integral, a generating function for the required expectation values, is defined, and four of the many possible decompositions of this function into cluster integrals are explored. Two of these decompositions are slight extensions of the conventional ones of Iwamoto and Yamada and Aviles, Hartogh, and Tolhoek. The other two are product decompositions, leading to new ``factor‐cluster'' formalisms. A factor‐cluster expansion is applied to the evaluation of the n‐particle spatial distribution function.