双曲群、四维流形与量子引力
Hyperbolic groups, 4-manifolds and Quantum Gravity
摘要：
4-流形具有特殊的拓扑性质，可以用来获得对量子力学的不同看法。一个重要的性质（与奇异的光滑性有关）是3-流形野生嵌入（亚历山大角球）的自然外观，它可以被解释为量子态。这种关系可以通过Turaev-Drinfeld量子化过程来证实。狂野嵌入的每一部分都承认双曲几何，揭示了量子力学和双曲几何之间的深层联系。然后，相应的对称性是用来得到一个从4到2的无穷曲率降维。物理后果将被讨论。最后，我们将得到一个几何量子态的时空表示，它是一个在无限曲率极限下稳定的非奇异分形空间（野嵌入）。
英文摘要：
4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders horned sphere) which can be interpreted as quantum states. This relation can be confirmed by using the Turaev-Drinfeld quantization procedure. Every part of the wild embedding admits a hyperbolic geometry uncovering a deep connection between quantum mechanics and hyperbolic geometry. Then the corresponding symmetry is used to get a dimensional reduction from 4 to 2 for infinite curvatures. Physical consequences will be discussed. At the end we will obtain a spacetime representation of a quantum state of geometry by a non-singular fractal space (wild embedding) which is stable in the limit of infinite curvatures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
