We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.
Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces
我们提出了一个新的应用程序的Regge-Teitelboim方法处理对称性的渐近定义。它可以被视为对他们1974年原始文件的补充。该制剂是基于取代渐近平面的两个--sheeted“沙漏”形的表面，通过加入顺利的传入双曲面与传出的。双曲面的半径是固定的，当人们沿着时间轴移动沙漏的中心时，就会覆盖整个时空。我们的动机是研究辐射，沙漏非常适合这项任务，因为它是渐近零的，因此能够记录过程的细节。给出了双曲面上场的一个简单的宇称条件。它规定了多少辐射进来就有多少辐射出去。利用它，我们导出了Bondi，van der Burg，Metzner和Sachs对称性的哈密顿形式，并将其应用于电磁场和引力场。这种结构必须具有渐近的电磁对偶性。对于引力，关于沙漏的线性化理论的公式还没有明确地构造出来，但是已经给出了足够的基础知识，以便能够建立主要的结果。给出了角动量守恒的定义（“磁扇区”是必不可少的）.它包含了自旋和电荷之间的相互关系。对于引力场，Taub-NUT空间表现为类似于磁极。
