圈量子引力中体积算符的性质 II:详细表述
广义相对论与量子宇宙学
2010-11-26 v2
摘要
我们首次在价数大于四的一般顶点上分析了由 Ashtekar 和 Lewandowski 构造的圈量子引力中体积算符的性质。本分析得益于 gr-qc/0405060 中推导出的体积算符矩阵元的一般简化公式,使得将其作为矩阵在计算机上实现并进行数值对角化成为可能。所得到的本征值可作为研究体积算符谱性质的数据库。本文还包含关于四价顶点谱的解析结果。本文是 arXiv:0706.0469 的姊妹篇,提供了其中分析工作的详细细节。
引用
@article{arxiv.0706.0382,
title = {Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation},
author = {Johannes Brunnemann and David Rideout},
journal= {arXiv preprint arXiv:0706.0382},
year = {2010}
}
备注
Companion to arXiv:0706.0469. Version as published in CQG in 2008. More compact presentation. Sign factor combinatorics now much better understood in context of oriented matroids, see arXiv:1003.2348, where also important remarks given regarding sigma configurations. Subsequent computations revealed some minor errors, which do not change qualitative results but modify some numbers presented here