论文标题
$ SO的几何参数化（D+1）$所有维循环量子重力的相位空间
Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity
论文作者
论文摘要
为了澄清$ SO（d+1）$ SPIN-NETWORD状态的几何信息，用于更高维度的循环量子重力，我们概括了$ su（2）$ su（2）$（1+3）$（1+3）$ dimensional loop量子的扭曲几何参数，以$（d+1）$ so（d+1）$ so so so so so so so so Plassionalsional caseensional casemensionalsionalsionsional casemensonsionalsions。关于扭曲的几何变量，泊松结构提出了一个新的量规程序，就统治理论运动学的离散的高斯和简单性约束而言。通过参数化赋予了几何含义，我们的还原过程旨在识别与异常离散的简单约束相关的适当规格自由，并随后导致（扭曲）离散ADM数据的所需经典状态空间。
To clarify the geometric information encoded in the $SO(D+1)$ spin-network states for the higher dimensional loop quantum gravity, we generalize the twisted-geometry parametrization of the $SU(2)$ phase space for $(1+3)$ dimensional loop quantum gravity to that of the $SO(D+1)$ phase space for the all-dimensional case. The Poisson structure in terms of the twisted geometric variables suggests a new gauge reduction procedure, with respect to the discretized Gaussian and simplicity constraints governing the kinematics of the theory. Endowed with the geometric meaning via the parametrization, our reduction procedure serves to identify proper gauge freedom associated with the anomalous discretized simplicity constraints and subsequently leads to the desired classical state space of the (twisted) discrete ADM data.
