Symmetries and canonical transformations in nuclei

We begin with a brief historical overview of the importance of special symmetries in atomic nuclei, especially the symplectic symmetry. We then show how deforming the symplectic algebra through canonical transformations that are unitary can be used to describe the same physics that in a non-deformed picture requires huge model spaces in far smaller deformed spaces, a simplification that should proportionally reduce the complexity of using the symplectic symmetry in applications. The overarching objective is to exploit this strategy to probe more deeply into the (ab initio) structure of nuclei, short cutting a need to await the development of evermore robust computational resources for carrying out advanced microscopic nuclear structure investigations.We begin with a brief historical overview of the importance of special symmetries in atomic nuclei, especially the symplectic symmetry. We then show how deforming the symplectic algebra through canonical transformations that are unitary can be used to describe the same physics that in a non-deformed picture requires huge model spaces in far smaller deformed spaces, a simplification that should proportionally reduce the complexity of using the symplectic symmetry in applications. The overarching objective is to exploit this strategy to probe more deeply into the (ab initio) structure of nuclei, short cutting a need to await the development of evermore robust computational resources for carrying out advanced microscopic nuclear structure investigations.