论文标题
量子时空的RICCI流动中的局部保形不稳定性和局部非碰撞
Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime
论文作者
论文摘要
众所周知，在量化一般相对论方面，路径积分方法中的保形不稳定性或无底问题上升。量子时空本身是否真的会遭受这种保形不稳定？如果是这样，保形不稳定性是否会导致局部时空区域的崩溃，甚至会导致整个时空崩溃？在量子时空参考框架（QSRF）和诱导时空RICCI流动的框架中研究了问题。我们发现，如果在局部紧凑型（封闭和有界）区域中与F功能相关的操作员的最低特征值是正的，则局部区域在共同状态下不稳定，并且倾向于沿着RICCI流动时T的体积变形和弯曲曲线；如果特征值为负或零，则局部区域在琐碎的恢复中稳定。但是，佩雷尔曼（Perelman）证明的RICCI流中的局部非collap曲，可确保不稳定性不会导致局部紧凑的时空区域崩溃。总的有效作用也被证明是从下面的正定义和界定的，使整个时空保持稳定，可以将其视为将重力定理的概括为量子水平的概括。
It is known that the conformal instability or bottomless problem rises in the path integral method in quantizing the general relativity. Does quantum spacetime itself really suffer from such conformal instability? If so, does the conformal instability cause the collapse of local spacetime region or even collapse the whole spacetime? The problems are studied in the framework of the Quantum Spacetime Reference Frame (QSRF) and induced spacetime Ricci flow. We find that if the lowest eigenvalue of an operator, associated with the F-functional in a local compact (closed and bounded) region, is positive, the local region is conformally unstable and will tend to volume-shrinking and curvature-pinching along the Ricci flow-time t; if the eigenvalue is negative or zero, the local region is conformally stable up to a trivial rescaling. However, the local non-collapsing theorem in the Ricci flow proved by Perelman ensures that the instability will not cause the local compact spacetime region collapse into nothing. The total effective action is also proved positive defined and bounded from below keeping the whole spacetime conformally stable, which can be considered as a generalization of the classical positive mass theorem of gravitation to the quantum level.
