2012/02/19 by Edward Anderson, Anderson, Edward
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1202.4187
openalex publication_date 2012/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I consider the momenta and conserved quantities for CP2 interpreted as the space of quadrilaterals. This builds on seminar I and II's kinematics via making use of MacFarlane's work considering the SU(3)-like (and thus particle physics-like) conserved 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. I study HO-like and highly symmetric potentials. I also provide 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 and for investigations of a number of Problem of Time strategies and of a number of other foundational and qualitative investigations of Quantum Cosmology.