论文标题
将公制的典范哈密顿量减少到其自然形式
Reduction of the canonical Hamiltonian of the metric GR to its natural form
论文作者
论文摘要
公制一般相对论的典范的哈密顿$ h_c $被降低为自然形式。典型的汉密尔顿人的自然形式在公制GR的实际应用中提供了许多优势，因为具有这样的汉密尔顿人的动力学系统的一般理论得到了很好的发展。此外，已经找到并详细描述了许多具有天然哈密顿量的动力学系统的分析和数值确切的解决方案。特别是，基于这一理论，我们可以讨论引力场与少数粒子系统之间的明显类比，其中粒子通过库仑或谐波电位相互连接。我们还开发了一种有效的方法，该方法用于确定动态变量的分析函数之间的各种泊松托。此外，可以从直接的动力学变量或双重组中选择这些变量，这些变量始终是在为度量引力开发的任何汉密尔顿公式中出现的。 PACS编号：04.20.FY和11.10.EF
The canonical Hamiltonian $H_C$ of the metric General Relativity is reduced to its natural form. The natural form of canonical Hamiltonian provides numerous advantages in actual applications to the metric GR, since the general theory of dynamical systems with such Hamiltonians is well developed. Furthermore, many analytical and numerically exact solutions for dynamical systems with natural Hamiltonians have been found and described in detail. In particular, based on this theory we can discuss an obvious analogy between gravitational field(s) and few-particle systems where particles are connected to each other by the Coulomb, or harmonic potentials. We also developed an effective method which is used to determine various Poisson brackets between analytical functions of the dynamical variables. Furthermore, such variables can be chosen either from the straight, or dual sets of symplectic dynamical variables which always arise in any Hamiltonian formulation developed for the metric gravity. PACS number(s): 04.20.Fy and 11.10.Ef
