Fractal Dimension in 3d Spin-Foams

Fractal Dimension in 3d Spin-Foams
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3d 旋转泡沫中的分形维数

DOI：
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发表时间：
2009
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通讯作者：
L. Modesto
L. Modesto
中科院分区：
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文献类型：
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作者：
F. Caravelli;L. Modesto

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本文利用Ponzano-Regge顶点动力学及其量子群推广（Turaev-Viro模型）计算了三维量子引力中时空的谱维数。我们认识到这一点，考虑一个非常简单的分解的三维时空，并引入一个边界状态，选择一个经典的几何边界。当探测标量场的能量从高能到低能逐渐减小时，时空的谱维从2变到3，穿过一个1.5相位。对于TV模型，高能谱维数随宇宙学常数的增大而增大。在低能量下，宇宙学常数的存在不会改变光谱维度。
In this paper we perform the calculation of the spectral dimension of the space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex (PR) and its quantum group generalization (Turaev-Viro model (TV)). We realize this considering a very simple decomposition of the 3d space-time and introducing a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the space-time runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decreases from high to low energy. For the TV model the spectral dimension at hight energy increase with the value of the cosmological constant. At low energy the presence of the cosmological constant does not change the spectral dimension.