Non-unitary evolution of noncommutative spaces and its application as models of the universe

非交换空间的非酉演化及其作为宇宙模型的应用

• 批准号: 16540244
• 负责人: SASAKURA Naoki
• 金额: $ 1.31万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540244/
• 关键词: Tensor model; Rank-three tensor; Fuzzy space; Quantum gravity; General relativity; Spacetime uncertainty relation; Vacuum energy; Dark energy; 非可換空間; ホップ代数; Twisted symmetry; Braided field theory; ダイナミカル; 非結合代数; 非可換幾何学; 一般座標変換; 非可換球面; 宇宙

Through the recent astrophysical observations, it has become clear that the most part of our universe is composed of the unidentified dark matter and dark energy. Especially the dark energy is a long-standing problem also in elementary particle physics, which is known as the cosmological constant problem or the vacuum energy problem. Probably, the solution requires the development of new quantum theory of gravity, which replaces the general relativity, the classical theory of gravity.General relativity is based on the concept of Riemannian geometry, and its dynamical variable is the metric tensor, which varies continuously on a coordinated spacetime. It is well known that the standard procedure of field quantization cannot be applied to the general relativity, because of the appearance of uncontrollable divergences. Moreover some thought experiments based on the general relativity and the quantum mechanics suggest the existence of the observable minimum length, and do not seem to favor the classical continuous and smooth spacetime. The concept of fuzzy spaces is an interesting candidate for such quantum spacetimes. In this granted project, I have pursued the possibilities to construct quantum gravity based on dynamical theory of filmy spaces. A fuzzy space can be defined by a rank-three tensor which determines the product rules among functions. Thus I have proposed dynamical theory of a rank-three tensor as that of fuzzy spaces. Such a rank-three tensor model is a background-independent theory which describes dynamical spaces of various topologies and dimensions in a unified manner. I have numerically studied the models, and have found that they can produce various physically meaningful spaces as classical solutions, and reproduces general relativity in the classical limit. Thus the rank-three tensor model provides an interesting candidate for quantum gravity well worth further study.

通过最近的天体物理学观测，我们已经清楚地知道，我们宇宙的大部分是由未知的暗物质和暗能量组成的。特别是暗能量在基本粒子物理学中也是一个长期存在的问题，它被称为宇宙常数问题或真空能量问题。很可能，解决方案需要发展新的量子引力理论，以取代经典的引力理论——广义相对论。广义相对论是建立在黎曼几何概念基础上的，它的动力学变量是度量张量，它在协调时空上连续变化。众所周知，由于不可控散度的出现，场量子化的标准程序不能应用于广义相对论。此外，一些基于广义相对论和量子力学的思想实验表明，存在可观测的最小长度，而似乎不支持经典的连续和光滑时空。模糊空间的概念是这种量子时空的一个有趣的候选者。在这个获得授权的项目中，我探索了基于薄膜空间动力学理论构建量子引力的可能性。模糊空间可以用一个三阶张量来定义，它决定了函数间的乘积规则。因此，我提出了三阶张量的动力学理论作为模糊空间的动力学理论。这种三阶张量模型是一种背景无关的理论，它统一地描述了各种拓扑和维度的动态空间。我对这些模型进行了数值研究，发现它们可以产生各种物理上有意义的空间作为经典解，并在经典极限下再现广义相对论。因此，秩三张量模型为量子引力提供了一个有趣的候选者，值得进一步研究。

项目成果

An invariant approach to dynamical fuzzy spaces with a three-index variable: Euclidean models

具有三指数变量的动态模糊空间的不变方法：欧几里得模型

• 发表时间: 2005
• 作者: Naoki;Sasakura;Naoki Sasakura;Naoki Sasakura;Naoki Sasakura;Naoki Sasakura
• 通讯作者: Naoki Sasakura

Braided quantum field theories and their symmetries

编织量子场论及其对称性

• 发表时间: 2007
• 期刊: Progress of Theoretical Physics 118
• 作者: Yuya Sasai;Naoki Sasakura
• 通讯作者: Naoki Sasakura

Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

非交换场论中的畴壁孤子和 Hopf 代数平移对称性

• 发表时间: 2008
• 期刊: Physical Review D 77
• 作者: Yuya Sasai;Naoki Sasakura
• 通讯作者: Naoki Sasakura

Heat kernel coefficients for compact fuzzy spaces

紧致模糊空间的热核系数

• 发表时间: 2004
• 期刊: Journal of High Energy Physics 0412
• 作者: Naoki;Sasakura;Naoki Sasakura;Naoki Sasakura;Naoki Sasakura;Naoki Sasakura
• 通讯作者: Naoki Sasakura

An Invariant approach to dynamical fuzzy spaces with a three-index variable : Euclidean models

具有三指数变量的动态模糊空间的不变方法：欧几里得模型

• 发表时间: 2006
• 期刊: The proceedings of 4th International Symposium on Quantum Theory and Symmetries (QTS-4) 2
• 作者: Yuya Sasai;Naoki Sasakura;Naoki Sasakura
• 通讯作者: Naoki Sasakura