Dynamical symmetries of BEC: exact energy formulas and an application to alpha-conjugate nuclei

An algebraic approach, based on dynamical symmetries, to Bose-Einstein condensates will be illustrated. It allows to write symmetry-dictated exact energy formulas for boson condensates that depend typically on a few quantum numbers. The application to alpha condensation in nuclei will be discussed in detail, showing that symmetry alone is sufficient to predict the energy of N-alpha states in alpha conjugate nuclei. Experiments that might improve the present knowledge will be suggested. (author)