论文标题
关于3D量子重力中量子组对称性的起源
On the origin of the quantum group symmetry in 3d quantum gravity
论文作者
论文摘要
众所周知，量子组与描述3D重力的量子状态有关。它们编码通过宇宙常数值参数量表对称的变形。它们通过量化Chern-Simons公式或Turaev-Viro的状态总和方法来表现为正则化的一种形式。由于该动作的定义是根据未变形的仪表不变性定义的，因此这种变形从连续和经典的图片中引起了困惑。我们在这里提出了一种新颖的方式，可以从第一原理和经典作用中衍生出这种量子组变形。该论点取决于两个主要步骤。首先，我们执行规范变换，该转换变形了仪表不变性和边界对称性，并使其依赖于宇宙常数。其次，我们实施了离散化程序，以依靠连续体的自由度的截断。
It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries parametrized by the value of the cosmological constant. They appear as a form of regularization either through the quantization of the Chern-Simons formulation or the state sum approach of Turaev-Viro. Such deformations are perplexing from a continuum and classical picture since the action is defined in terms of undeformed gauge invariance. We present here a novel way to derive from first principle and from the classical action such quantum group deformation. The argument relies on two main steps. First we perform a canonical transformation, which deformed the gauge invariance and the boundary symmetries, and makes them depend on the cosmological constant. Second we implement a discretization procedure relying on a truncation of the degrees of freedom from the continuum.
