Dynamical symmetries in contemporary nuclear structure applications

In terms of group theory—the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of group-subgroup structures that define the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems. We review two types of applications of dynamical symmetries in contemporary theoretical nuclear structure physics: first for a classification of the many-body systems under consideration, with respect to an important characteristic of their behavior; and second for the creation of exactly solvable algebraic models that describe specific aspects of this behavior. This is illustrated with the boson and fermion realizations of symplectic structures. In the first case with an application of the sp(4, R) classification scheme of even-even nuclei within the major nuclear shells and next with of the sp(4) microscopic model for the description of isovector pairing correlations.