Boson-fermion realization of lie algebras and dynamical supersymmetry in fermion systems

Recent experimental results by Metz, Jolie and collaborators have led to renewed interest in the notion of dynamical supersymmetry in fermion many-body systems. By considering the general problem of constructing a boson-fermion realization for Lie algebras with generators expressed in terms of fermion and bifermion operators, also when favoured pairs dictate the structure of collective bosons, we demonstrate that dynamical "supersymmetry without bosons" can indeed emerge in a fermion system without any Pauli violations. Our construction of the general realization utilises the identification of a physical subspace and allows one to identify the images of single particle transfer operators uniquely, unlike the situation in phenomenological applications of dynamical supersymmetry.