Assuming the ground state wavefunction, #,, , of a boson fluid is known, and writing the excited state wavefunctions in the form F/J,, , a linear eigenvalue equation of the form l?F = tPF is obtained, where E0 + E is the excited state energy, E0 is the ground state energy, and His a non-hermitian operator which depends in a simple way upon U = In $2 instead of the potential energy function. An extremum principle is derived in terms of an auxiliary hermitian Hamiltonian operator, H'. The many-body boson plane-wave basis, {P,& ... k,)) is used to express U in terms of its Fourier components (ordered conveniently in terms of the number of nonzero arguments), making it possible to calculate matrix elements of Z? and H' in that basis. A perturbation theory similar to Brillouin-Wigner perturbation theory is developed for the non-hermitian eigenvalue problem. Nonorthogonal perturbation theory is developed for the correlated basis {p 4 n J. The requirement that these two perturbation theories be consistent produces useful relationships between the components of U and the static structure functions of &, . These relationships are shown to reduce to previous results in the extreme case of low density and weak interactions.