  Cumulants represent a natural language for expressing macroscopic properties
of a solid. We show that cumulants are subject to a nontrivial geometry. This
geometry provides an intuitive understanding of a number of cumulant relations
which had been obtained so far by using algebraic considerations. We give
general expressions for their infinitesimal and finite transformations and
represent a cumulant wave operator through an integration over a path in the
Hilbert space. Cases are investigated where this integration can be done
exactly. An expression of the ground-state wavefunction in terms of the
cumulant wave operator is derived. In the second part of the article we derive
the cumulant counterpart of Faddeev`s equations and show its connection to the
method of increments.
