论文标题
依赖位置的质量量子系统和ADM形式主义
Position-Dependent Mass Quantum systems and ADM formalism
论文作者
论文摘要
一般相对论（GR）的经典爱因斯坦 - 希尔伯特（EH）作用与具有位置依赖性质量（PDM）模型的经典系统正式相似。该类比是开发并用于建立协变性古典哈密顿式的，并定义了GR的替代阶段肖像。相位空间中相关的汉密尔顿方程组作为爱因斯坦磁场方程双重的一阶系统表示。遵循量子力学的原则，我为经典将军建立了一个规范的理论。基于采用高维相空间，构建了完全一致的GR量子Hamiltonian。观察到功能波方程是永恒的。作为直接应用，我提出了量子宇宙学的替代波方程。与标准的Arnowitt-Deser-Misner（ADM）分解和量子重力提案相比，当将指标分解为$ 3+1 $尺寸ADM分解时，我将分析扩展到协方差范围。我表明，如果使用ADM分解度量，则可以获得相等的尺寸空间。
The classical Einstein-Hilbert (EH) action for general relativity (GR) is shown to be formally analogous to the classical system with position-dependent mass (PDM) models. The analogy is developed and used to build the covariant classical Hamiltonian as well as defining an alternative phase portrait for GR. The set of associated Hamilton's equations in the phase space is presented as a first-order system dual to the Einstein field equations. Following the principles of quantum mechanics, I build a canonical theory for the classical general. A fully consistent quantum Hamiltonian for GR is constructed based on adopting a high dimensional phase space. It is observed that the functional wave equation is timeless. As a direct application, I present an alternative wave equation for quantum cosmology. In comparison to the standard Arnowitt-Deser-Misner(ADM) decomposition and quantum gravity proposals, I extended my analysis beyond the covariant regime when the metric is decomposed into the $3+1$ dimensional ADM decomposition. I showed that an equal dimensional phase space can be obtained if one applies ADM decomposed metric.
