arXiv 1202.41872012-02gr-qc

关系四边形同位旋与超荷的类比

Relational Quadrilateralland. Analogues of Isospin and Hypercharge

Edward Anderson

备注：: 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

摘要：

我考虑了在四边形空间中CP ^2的动量和守恒量。这是建立在Seminar I和II的运动学基础上的，通过利用麦克法兰的工作，考虑了CP ^[2]中出现的类SU（3）（因此也是类粒子物理）守恒量。我执行的额外步骤，进一步解释为所有关系四边形的配置空间，从而为整个宇宙，关系和几何动力学模拟物理一个有趣的玩具模型。我还提供了四边形的Kuchar观测量，这是一个特殊的解决方案的问题的观测量。我研究HO样和高度对称的潜力。我还提供了CP ^2上动力学的一些精确解和定性行为。在每一种情况下，我重新解释的结果在quadrature。这为关系四边形的量子力学研究和一些时间问题策略的研究以及量子宇宙学的一些其他基础和定性研究铺平了道路。

英文摘要：

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.

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