标题： 量子等效磁场而非经典等效磁场 显示英文标题

标题： Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

摘要： 我们构造了紧致Kähler-Einstein流形对$(M_i,g_i,\omega_i)$($i=1,2)$的复数维数为$n$，具有以下性质：规范线丛$L_i=\bigwedge^n T^*M_i$的陈类为$[\omega_i/2\pi]$，并且对于每个整数$k$，张量幂$L_1^{\otimes k}$和$L_2^{\otimes k}$对于与规范连接相关的丛拉普拉斯算子是等谱的，而$M_1$和$M_2$-- 因此$T^*M_1$和$T^*M_2$-- 不同胚。 在几何量子化的背景下，我们将这些例子解释为磁场所示，它们是量子等价的但不是经典等价的。 此外，我们构造了许多线丛$L$的例子，基流形上的势对$Q_1$，$Q_2$，以及在$L$上的连接对$\nabla_1$，$\nabla_2$，使得对于每个整数$k$，在$L^{\otimes k}$上相关的薛定谔算子是等谱的。 显示英文摘要

摘要： We construct pairs of compact K\"ahler-Einstein manifolds $(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class $[\omega_i/2\pi]$, and for each integer $k$ the tensor powers $L_1^{\otimes k}$ and $L_2^{\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_1$ and $M_2$ -- and hence $T^*M_1$ and $T^*M_2$ -- are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent. Moreover, we construct many examples of line bundles $L$, pairs of potentials $Q_1$, $Q_2$ on the base manifold, and pairs of connections $\nabla_1$, $\nabla_2$ on $L$ such that for each integer $k$ the associated Schr\"odinger operators on $L^{\otimes k}$ are isospectral.