论文标题
多边形的量子重力和$ \ bbb r \ times \ bbb z_n $ flrw型号
Quantum gravity on polygons and $\Bbb R\times \Bbb Z_n$ FLRW model
论文作者
论文摘要
我们将$ \ bbb z_n $的量子几何形状作为一个多边形图，边缘上有任意度量长度，找到了$*$ - 保存量子Levi-civita连接，该连接是$ n \ ne 4 $唯一的。作为第一个应用程序，我们在$ \ bbb z_n $上计算欧几里得量子重力的数值相关函数，用于小$ n $。然后，我们在$ \ bbb r \ times \ bbb z_n $上研究FLRW模型，在1+2维中找到与经典FLRW模型相同的扩展率。我们还在$ \ bbb r \ times \ bbb z_n $上查看粒子的创建，并找到一个额外的$ m = 0 $绝热无粒子创建扩展以及粒子创建频谱，以进行平滑的步骤扩展。
We fully solve the quantum geometry of $\Bbb Z_n$ as a polygon graph with arbitrary metric lengths on the edges, finding a $*$-preserving quantum Levi-Civita connection which is unique for $n\ne 4$. As a first application, we numerically compute correlation functions for Euclideanised quantum gravity on $\Bbb Z_n$ for small $n$. We then study an FLRW model on $\Bbb R\times\Bbb Z_n$, finding the same expansion rate as for the classical flat FLRW model in 1+2 dimensions. We also look at particle creation on $\Bbb R\times \Bbb Z_n$ and find an additional $m=0$ adiabatic no particle creation expansion as well as the particle creation spectrum for a smoothed step expansion.
