标题： 宇宙弦模型的规范量子化 显示英文标题

标题： Canonical Quantization of the Gowdy Model

摘要： 研究了具有三维环面空间拓扑的Gowdy宇宙家族，既从经典角度又从量子力学角度进行研究。 从Lorentzian广义相对论的Ashtekar表述出发，我们引入了一个规范固定过程，以消除几乎所有的非物理自由度。 这样，我们得到一个仅受一个均匀约束的约化模型。 该模型的相空间通过一组规范的基本变量来描述。 这些变量包括两个实数均匀变量，以及四个在不对应于Gowdy时空的Killing场的角坐标上周期性的实数场的傅里叶系数。 我们还得到了线元和约化哈密顿量的显式表达式。 随后，我们通过将基本变量表示为作用于解析泛函向量空间上的线性算子来对系统进行量子化。 该空间上的内积通过施加Lorentzian现实条件来选择。 我们找到了被代表模型的均匀约束的算子湮灭的量子态，并用它们构建物理态的Hilbert空间。 最后，我们推导出该模型的量子可观测量的一般形式。 显示英文摘要

摘要： The family of Gowdy universes with the spatial topology of a three-torus is studied both classically and quantum mechanically. Starting with the Ashtekar formulation of Lorentzian general relativity, we introduce a gauge fixing procedure to remove almost all of the non-physical degrees of freedom. In this way, we arrive at a reduced model that is subject only to one homogeneous constraint. The phase space of this model is described by means of a canonical set of elementary variables. These are two real, homogeneous variables and the Fourier coefficients for four real fields that are periodic in the angular coordinate which does not correspond to a Killing field of the Gowdy spacetimes. We also obtain the explicit expressions for the line element and reduced Hamiltonian. We then proceed to quantize the system by representing the elementary variables as linear operators acting on a vector space of analytic functionals. The inner product on that space is selected by imposing Lorentzian reality conditions. We find the quantum states annihilated by the operator that represents the homogeneous constraint of the model and construct with them the Hilbert space of physical states. Finally, we derive the general form of the quantum observables of the model.