论文标题
非扰动量子重力中的广义光谱尺寸
Generalised spectral dimensions in non-perturbative quantum gravity
论文作者
论文摘要
在非扰动性重力理论中，看似普遍的有效尺寸的现象已被证明是量子重力现象学的潜在来源。仅考虑标量场的量度依赖性有效维度。但是，有可能出现在普朗克量表附近的非曼佛像结构的有效维度可能取决于所考虑的场的类型。为了研究这个问题，我们研究了与Laplace-Beltrami运算符相关的光谱维度，该频谱在非扰动模型的空间切片上概括为$ k $ - 形式，称为因果动力学三角形。我们发现，两种形式的张量和双标量光谱尺寸显示出有效尺寸的两个尺度之间的流动。但是，单一形式和矢量光谱尺寸仅显示一个有效的维度。单形和矢量光谱维度没有显示有效维度流的事实可能与电磁场的分散关系不存在有关，而是动态生成而不是作为假设。
The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension from quantum gravity has only been considered for scalar fields. It is however possible that the non-manifold like structures, that are expected to appear near the Planck scale, have an effective dimension that depends on the type of field under consideration. To investigate this question, we have studied the spectral dimension associated to the Laplace-Beltrami operator generalised to $k$-form fields on spatial slices of the non-perturbative model of quantum gravity known as Causal Dynamical Triangulations. We have found that the two-form, tensor and dual scalar spectral dimensions exhibit a flow between two scales at which an effective dimension appears. However, the one-form and vector spectral dimensions show only a single effective dimension. The fact that the one-form and vector spectral dimension do not show a flow of the effective dimension can potentially be related to the absence of a dispersion relation for the electromagnetic field, but dynamically generated instead of as an assumption.
