Berakdar, J.

A scheme is presented for expressing the many-body Green operator of an interacting system in terms of Green operators of systems with a fewer number of interacting particles. The method relies on an exact algebraic operator identity proved in this work. Furthermore, we present a hierarchical approximation that reduces successively the many-body problem to a lower dimensional solvable problem. Recipes for higher order corrections are given and practical applications are pointed out.

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