Boson-fermion Dyson mapping and supersymmetry in fermion systems

Abstract

We demonstrate that exact supersymmetry can emerge in a purely fermionic system. This "supersymmetry without bosons" is unveiled by constructing a novel boson-fermion Dyson mapping from a fermion space to a space comprised of collective bosons and ideal fermions. In a nuclear structure context the collective spectra of even and odd nuclei can then be unified in a supersymmetric description with Pauli correlations still exactly taken into account.