RELATIONAL QUADRILATERALLAND. II. ANALOGUES OF ISOSPIN AND HYPERCHARGE

I consider the momenta and conserved quantities for CP2 interpreted as the space of quadrilaterals. This builds on Paper I’s kinematics via making use of MacFarlane’s work considering the SU(3)-like (and thus particle physics-like) con-served quantities that occur for CP2. I perform the additional step of further interpreting that as the configuration space of all relational quadrilaterals and thus an interesting toy model for whole-universe, relational and geometrodynamical-analogue physics. I also provide the Kuchar ̌ observables for the quadrilateral, which is a particular resolution of the Problem of Observables based on Paper I and II’s results. I study HO-like and highly symmetric potentials. I also some some exact solutions and qualitative behaviours for dynamics on CP2. In each case, I reinterpret the results in terms of quadrilaterals. This paves the way for the quantum mechanical study of the relational quadrilateral in Paper III and for investigations of a number of Problem of Time strategies (mostly in Paper IV) and of a number of other foundational and qualitative investigations of Quantum Cosmology. PACS: 04.60Kz