Interdisciplinary Center for Theoretical Study, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev Lett. 2015 Sep 18;115(12):121601. doi: 10.1103/PhysRevLett.115.121601. Epub 2015 Sep 15.
We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau threefolds. Our proposal includes all contributions to the energy spectrum which are nonperturbative in the Planck constant, and is much simpler than the available quantization condition in the literature. We check that our proposal is consistent with previous works and implies nontrivial relations among the topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries. Together with the recent developments, our proposal opens a new avenue in the long investigations at the interface of geometry, topology and quantum mechanics.
我们提出了一类来源于局部环面 Calabi-Yau 三维流形的量子力学系统的新的精确量子化条件。我们的建议包括对普朗克常数是非微扰的所有对能谱的贡献，并且比文献中现有的量子化条件简单得多。我们验证了我们的建议与以前的工作是一致的，并暗示了环面 Calabi-Yau 几何的拓扑 Gopakumar-Vafa 不变量之间的非平凡关系。结合最近的发展，我们的建议为几何、拓扑和量子力学的界面的长期研究开辟了新的途径。
