Representations of Three-Body Interactions In Physics

Abstract: The thesis explores an already developed symmetry adapted representation of a two-body interaction with the main goal of extending the method to also include three-body interactions. The method considers a space of shifted one dimensional Gaussian particle densities which are used, together with their corresponding Hartree potentials, to define the respective collective subspaces in which the interactions are expanded. The performance of the method is then examined by how much the interactions can be compressed at the expense of the resolution in the potential energy of particle densities modeled by one dimensional Gaussian distributions. By compression, the percentage reduction in numerical calculations is meant. The result shows that the method is successful in compressing two and three-body interactions by about 94 and 97 % respectively, while still allowing the interactions to be fully recovered in their collective subspaces.