Dynamical superalgebra and supersymmetry for a many-fermion system.

A linearization scheme is proposed for the general Hamiltonian of an interacting fermion system, consisting of a mean-field approximation in which pairing and umklapp play dominant roles. A variety of models emerge, characterized by a hierarchy of spectrum-generating algebras and superalgebras, of which some are supersymmetric. The superconducting phase transition is shown to be related to supersymmetry breaking.