Title: Quantum Degenerate Systems Show Chinese title

Title: 量子退化系统

Abstract: Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems --in which the degeneracy cannot be eliminated by redefining variables in the action--, the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated. Show Chinese abstract

Abstract: 退化动力学系统的特点是其相空间中的辛结构的秩在整个相空间内不恒定。其相空间被划分为因果上不相连且互不重叠的区域，使得不存在连接两个不同区域的经典轨道。这里讨论的问题是这种经典上的不连通性在量子化后是否仍然存在。我们的结论是，在不可约退化系统中——即通过在作用量中重新定义变量无法消除退化的情况下——这种不连通性在量子理论中得以保持：在退化面上不存在量子隧穿现象。这表明退化面是分离不同物理系统的边界，不仅在经典意义上如此，在量子领域同样如此。这一特征对于引力和高维 Chern-Simons 理论的重要性不容忽视。