标题： 陈-西蒙斯不变量作为经典和量子宇宙学的自然时间变量 显示英文标题

标题： The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology

摘要： 我们提出，Ashtekar-Sen联络的Chern-Simons不变量是经典和量子宇宙学的自然内部时间坐标。 这种功能具有一系列有趣的性质，这里我们将对其进行描述。 1）它是一个规范和微分同胚不变构型空间上的函数，在由广义相对论的Ashtekar形式定义的度规下，其梯度正交于两个物理自由度。 2）当宇宙常数接近零，$\Lambda$，且解接近DeSitter时空时，Chern-Simons形式的虚部归约为York外延时间坐标。 3）由于量子约束，Chern-Simons态的小物质场激发满足一个函数Schroedinger方程，其中物质场在Chern-Simons时间内演化于DeSitter背景上。 然后我们提议这是对于$\Lambda \neq 0$的理论的自然真空态。 4）由于大规范变换，这个时间坐标在欧几里得化时空的构型空间上是周期性的，这意味着非微扰量子引力中所有状态的物理期望值都将满足$KMS$条件，并可以解释为热态。 5）支持这一提议的物理哈密顿量和内积形式被建议，同时发现了一个新的广义相对论作用原理，即连接超空间上的测地线原理。 显示英文摘要

摘要： We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, $\Lambda$, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for $\Lambda \neq 0$. 4)This time coordinate is periodic on the configuration space of Euclideanized spacetimes, due to the large gauge transformations, which means that physical expectation values for all states in non-perturbative quantum gravity will satisfy the $KMS$ condition, and may then be interpreted as thermal states. 5)Forms for the physical hamiltonians and inner product which support the proposal are suggested, and a new action principle for general relativity, as a geodesic principle on the connection superspace, is found.