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首页> 外文期刊>Classical and Quantum Gravity: An Interantional Journal of Gravity Geometry of Field Theories Supergravity Cosmology >Area propagator and boosted spin networks in loop quantum gravity
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Area propagator and boosted spin networks in loop quantum gravity

机译：区域传播者和环路量子重力的增强自旋网络

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摘要

Quantum states of geometry in loop quantum gravity are defined as spin networks, which are graph dressed with SU(2) representations. A spin network edge carries a half-integer spin, representing basic quanta of area, and the standard framework imposes an area matching constraint along the edge: it carries the same spin at its source and target vertices. In the context of coarse-graining, or equivalently of the definition of spin networks as projective limits of graphs, it appears natural to introduce excitations of curvature along the edges. An edge is then treated similarly to a propagator living on the links of Feynman diagrams in quantum field theory: curvature excitations create little loops -tadpoles- which renormalize it. This relaxes the area matching condition, with different spins at both ends of the edge. We show that this is equivalent to combining the usual SU(2) holonomy along the edge with a Lorentz boost into SL(2, C) group elements living on the spin network edges, underlining the fact that the Ashtekar-Barbero connection carries extrinsic curvature degrees of freedom. This finally leads us to introduce a new notion of area waves in loop quantum gravity.
机译：环形量子重力的几何形状的量子状态被定义为旋转网络，这是用SU（2）表示的图形。自旋网络边缘携带半整数旋转，代表面积的基本量子，标准框架沿边缘施加一个区域匹配约束：它在其源极和目标顶点上携带相同的旋转。在粗谷物的背景下，或等效自旋网络的定义作为图的投影限制，它看起来自然地引入沿边缘的曲率激动。然后将边缘与生活在Quantum场理论中的Feynman图联系的传播者相似：曲率激励会产生很少的循环 - 这使其重整。这放宽了区域匹配条件，边缘两端具有不同的旋转。我们认为，这相当于将沿着边缘的通常苏（2）与Lorentz Boost沿着生活在旋转网络边缘上的SL（2，C）组元素组合，强调了Ashtekar-Barbero连接带有外部曲率的事实自由程度。这最终导致我们引入环形量子重力的区域波的新概念。

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