标题： 广义协变性、环圈与物质 显示英文标题

标题： General covariance, loops and matter

摘要： 本文提出了一种四维广义协变场论，描述了与标量场耦合的非动力学三维几何。 该理论具有无穷多个物理可观测量（或运动常数），这些可观测量由标量场构型组成的环构建而成。 这些可观测量的泊松代数是闭合的，并且与阿什图卡尔形式主义中的3+1引力环变量相同。 该理论还具有给出开曲面面积和有限区域体积的可观测量。 给出了该理论的所有哈密顿-雅可比方程以及坐标表示下的狄拉克量子化条件的解。 这些解基于物质环的平行传输子。 还简要讨论了量子理论的环空间表示及其对3+1引力量子化的某些影响。 显示英文摘要

摘要： A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are constructed from loops made from scalar field configurations. The Poisson algebra of these observables is closed and is the same as that for the 3+1 gravity loop variables in the Ashtekar formalism. The theory also has observables that give the areas of open surfaces and the volumes of finite regions. Solutions to all the Hamilton-Jacobi equations for the theory and the Dirac quantization conditions in the coordinate representation are given. These solutions are holonomies based on matter loops. A brief discussion of the loop space representation for the quantum theory is also given together with some implications for the quantization of 3+1 gravity.