标题： 一维离散引力 显示英文标题

标题： Discrete Gravity in One Dimension

摘要： 讨论了一种基于Regge引力离散形式的一维（时间）量子引力模型。研究了精确连续晶格微分同胚的性质及其对正则化引力测度的影响。在引入与边长耦合的无质量标量场后，在有限晶格上精确地进行了标量泛函积分，并确定了测度的变化。发现由于标量场涨落导致的宇宙学常数的重整化在二维中恒等于零。对配分函数进行了简单的缩放重整化群变换，并将结果与精确解进行比较。最后，将标量拉普拉斯算子谱的性质与边长的泊松分布所得结果进行了比较。 显示英文摘要

摘要： A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are examined. After introducing a massless scalar field coupled to the edge lengths, the scalar functional integral is performed exactly on a finite lattice, and the ensuing change in the measure is determined. It is found that the renormalization of the cosmological constant due to the scalar field fluctuations vanishes identically in one dimension. A simple decimation renormalization group transformation is performed on the partition function and the results are compared with the exact solution. Finally the properties of the spectrum of the scalar Laplacian are compared with results obtained for a Poissonian distribution of edge lengths.