A New formulation of Quantum Gravity

量子引力的新表述

基本信息

批准号：
09640330
负责人：
KAWAMOTO Noboru
金额：
$ 1.86万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640330/
关键词：
quantum gravity generalized gauge theory Lattice gravity N=2 super symmetry Chern-Simons action fructral structure C=-2 model BF theory Quantum gravity Super Yang-Mills Lattice gravity RF theory Dirac-Kahlerfermion Chern-Simons A

项目摘要

I have been working on the following four subjects under the above project : 1) We proposed (Kawamoto, Watabiki) new type of generalized gauge theories which could be formulated in any dimensions about 10 years ago. We quantized the generalized Chern-Simons action and found out that the system is infinitely reducible and can be quantized by introducing infinitely many ghosts yet has the same Chern-Simons form as the original classical action. We have then quantized the generalized topological Yang-Mills action with instanton gauge fixing and found that N=2 super-Yang-Mills action comes out as a natural consequence of the the quantization via twisting procedure. We found the twinsting is essentitally related with Dirac-Kahler fermion formulation. 2) We have successfully formulated the three-dimensional Chern-Simons gravity on the random lattice. It turned out that the model is equivalent with the Ponzano-Regge model. We have then successfully applied this formulation into four dimensional BF gravity on the random lattice. 3) We have investigated two dimensional quantum gravity coupled c=-2 matter numerically with great accuracy. We have learned that the essense of the two dimensional quantum gravity is the fractal nature and the numerical fractal dimensions are consistent with the theoretical prediction. The three dimensional extension of this model is investigated numerically. We measured the string susceptibility and found an evidence that there exists a continuum limit of the three dimensional lattice gravity. 4) We have extended the generalized gauge theory to formulate the generalized Yang-Mills action and applied to formulate Weinberg-Salam model successfully by using SU(2|1) super group.

在上述项目下，我一直在研究以下四个课题：1）大约10年前，我们提出了（Kawamoto，Watabiki）新型广义规范理论，该理论可以在任何维度上表述。我们对广义陈-西蒙斯作用进行了量化，发现该系统是无限可约的，可以通过引入无限多个鬼魂来量化，但具有与原始经典作用相同的陈-西蒙斯形式。然后，我们用瞬子规范固定来量化广义拓扑杨米尔斯作用，并发现 N=2 超杨米尔斯作用是通过扭转过程进行量化的自然结果。我们发现孪生本质上与狄拉克-卡勒费米子公式有关。 2）我们成功地在随机晶格上表述了三维陈-西蒙斯引力。事实证明，该模型与 Ponzano-Regge 模型等效。然后我们成功地将这个公式应用到随机晶格上的四维 BF 引力中。 3）我们以高精度数值研究了二维量子引力耦合c=-2物质。我们知道，二维量子引力的本质是分形性质，分形数值维数与理论预测一致。对该模型的三维扩展进行了数值研究。我们测量了弦的磁化率，并发现了三维晶格引力存在连续极限的证据。 4）我们扩展了广义规范理论来制定广义Yang-Mills作用，并利用SU(2|1)超群成功地制定了Weinberg-Salam模型。