圈引力的变形旋量网络：双曲扭曲几何
Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
摘要：
在广义相对论的正则量子化的背景下，我们可以通过用SL（2，C）代替与每条边相连的T*SU（2）相空间来变形图上的圈引力相空间。这种变形被认为是对非零宇宙学常数的存在进行编码。在这里，我们展示了如何用旋量变量来参数化这个相空间，从而得到圈引力的变形旋量网络，在顶点处有规范群SU（2）的变形作用量。这些被正式解释为圈重力扭曲几何的推广到双曲曲率。
英文摘要：
In the context of a canonical quantization of general relativity, one can deform the loop gravity phase space on a graph by replacing the T*SU(2) phase space attached to each edge by SL(2,C) seen as a phase space. This deformation is supposed to encode the presence of a non-zero cosmological constant. Here we show how to parametrize this phase space in terms of spinor variables, thus obtaining deformed spinor networks for loop gravity, with a deformed action of the gauge group SU(2) at the vertices. These are to be formally interpreted as the generalization of loop gravity twisted geometries to a hyperbolic curvature.
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