The Feynman path-integral formulation is used to analyze the grand-partition function Z and the n-body Green's function Gn or rather their cumulants (or connected parts) G̃n for a system governed by p-body interaction potentials vp. It is shown that the functional relationship expressing G̃n in terms of vp is invariant under the transformation exchanging −(−)mG̃m and vm everywhere. Under the same transformation log Z undergoes a change of sign. The content of these results is discussed in conclusion.
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Dominicis et al. (1967) studied this question.
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