Dynamical symmetries in collective nuclear stuctures

The concept of dynamical symmetries for nuclear physics is reviewed. The two main schools of thought, IBM'S and Elliott's are contrasted. The primary difference between these two is that for the IBM, the proposed multi-chain dynamical symmetries are experimentally detectable while for the Elliott's school, a mono-chain SU(3) is proposed as a way to choose a Hilbert space where rotational collectivity is built-in. Also, geometrization of the IBM via coherent states is discussed in detail. Finally, it is shown that the profound concept of multi-chain dynamical symmetries unraveled by the IBM is the key ingredient for a recently developed dermion dynamical symmetry model (FDSM). This model which unifies the high as well as low spin collective states, amalgamates both schools of thought