Relational Quadrilateralland. Analogues of Isospin and Hypercharge
Abstract
I consider the momenta and conserved quantities for CP^2 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 CP^2. 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 CP^2. 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.
Cite
@article{arxiv.1202.4187,
title = {Relational Quadrilateralland. Analogues of Isospin and Hypercharge},
author = {Edward Anderson},
journal= {arXiv preprint arXiv:1202.4187},
year = {2013}
}
Comments
Seminar III on relational quadrilaterals (2-d 4-body problem as a whole-universe model free from absolute structure). References updated and minor typos removed. arXiv admin note: substantial text overlap with arXiv:1202.4186