论文标题
广告上的分数klein-gordon方程$ _ {2+1} $
Fractional Klein-Gordon Equation on AdS$_{2+1}$
论文作者
论文摘要
我们提出了对分数klein-gordon方程的协变量定义，其远程相互作用与基础歧管的度量无关。作为一个例子，我们考虑ADS $ _ {2+1} $上的分数klein-gordon方程，计算分数Laplace-Beltrami操作员的显式内核表示以及分数Klein-Gordon方程的两点传播器。我们的结果表明，仅当质量与逆广告半径相比，传播器仅存在质量，这可能是因为广告空间以距离作为相同尺寸的平坦空间更快地扩展。我们的结果预计将特别适用于统计力学和量子信息中的AD/CFT对应的新应用。
We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent of the metric of the underlying manifold. As an example we consider the fractional Klein-Gordon equation on AdS$_{2+1}$, computing the explicit kernel representation of the fractional Laplace-Beltrami operator as well as the two-point propagator of the fractional Klein-Gordon equation. Our results suggest that the propagator only exists if the mass is small compared to the inverse AdS radius, presumably because the AdS space expands faster with distance as a flat space of the same dimension. Our results are expected to be useful in particular for new applications of the AdS/CFT correspondence within statistical mechanics and quantum information.
