1202.4187 (Edward Anderson)

Relational Quadrilateralland. II. Analogues of Isospin and Hypercharge    [PDF]

Edward Anderson

I consider the momenta and conserved quantities for CP^2 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)
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 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 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 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.

View original: http://arxiv.org/abs/1202.4187