连续统随机梳与尺度相关谱维数
Continuum Random Combs and Scale Dependent Spectral Dimension
摘要：
数值计算表明，在因果动力学三角模型的量子引力的有效尺寸的时空在紫外线低于在IR。在本文中，我们开发了一个简单的模型的基础上以前的工作随机梳，共享的一些性质的CDT，在这种效果可以被证明是发生解析。我们构造了一个短距离和长距离的谱维数的定义，并表明随机梳模型表现出尺度依赖的谱维数以这种方式定义。我们还观察到，一个层次的表观光谱尺寸可以得到在UV和IR制度之间的交叉区域的连续变量的适当选择。我们的主要结果是有效的广泛的一类齿长分布，从而扩展以前的工作随机梳Durhuus等人。
英文摘要：
Numerical computations have suggested that in causal dynamical triangulation models of quantum gravity the effective dimension of spacetime in the UV is lower than in the IR. In this paper we develop a simple model based on previous work on random combs, which share some of the properties of CDT, in which this effect can be shown to occur analytically. We construct a definition for short and long distance spectral dimensions and show that the random comb models exhibit scale dependent spectral dimension defined in this way. We also observe that a hierarchy of apparent spectral dimensions may be obtained in the cross-over region between UV and IR regimes for suitable choices of the continuum variables. Our main result is valid for a wide class of tooth length distributions thereby extending previous work on random combs by Durhuus et al.
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