  Starting from a general, microscopic fermion-to-boson mapping that preserves
Hermitian conjugation, we discuss truncations of the boson Fock space basis. We
give conditions under which the exact boson images of finite fermion operators
are also finite (e.g., a 1+2-body fermion Hamiltonian is mapped to a 1+2-body
boson Hamiltonian) in the truncated basis. For the most general case, where the
image is not necessarily exactly finite, we discuss how to make practical and
controlled approximations.
