A perturbation theory is developed for the logarithm of the normalization integral (or partition function) of an N-body system which is either a Bose liquid in its ground state or a classical fluid in the canonical ensemble. The perturbation in the former is an n-body factor in the ground state wavefunction and in the latter is an n-body potential. The normalization function serves as a generating function for the cumulants (or static correlation functions) of the density fluctuation operator ρk. The expansions of the perturbed partition function and correlation functions are shown to be linked cluster expansions involving the correlation functions in the unperturbed system; each term in these expansions is manifestly of the proper order in N. Several approximations involving truncations of the cumulants and/or resummation of part of the terms in the linked cluster expansions are discussed.
Linked-cluster expansion for a degenerate system is formulated so that it could be widely applicable to nuclear shell model calculation. Most parts of discussion are given to operation of linking. The model space is extended to any number of valence particles being coupled to an inert or a dynamically active core. The J-scheme is adopted and restriction of Pauli principle is maintained in a maximum possible way as allowed by operations of linking and folding. It reduces the number of diagrams. Algebraic expression for the linked diagram of unfolded form is derived in two ways. One is by means of a relation among cfp's and the other relies on a generalized commutation relation.