Fermion-boson interactions and quantum algebras

Quantum algebras $(q$ algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a ${\mathrm{su}}_{q}(2)$ dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and bosons interacting via schematic forces. The structure of the proposed ${\mathrm{su}}_{q}(2)$ Hamiltonians, and the meaning of the corresponding deformation parameters, are discussed.