A fermion mapping of boson-fermion pairs is proposed. The mapping is applied to an exactly solvable two-level test model and shown to be useful for treating strong boson-fermion correlations in quantum systems.
I derive in a novel fashion exact formulas for the calculation of general matrix elements, including the overlap (norm) matrix, between states constructed from fermion pairs. Mapping the fermion pairs to bosons, I show how to construct finite and exact (in the sense of preserving matrix elements) boson representations of the norm operator and one- and two-fermion operators. This may lead to a microscopic basis for the Interacting Boson Model, as well as new truncation schemes for the nuclear shell model.