论文标题
在Hofer-Zehnder的能力上
On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces
论文作者
论文摘要
我们确定了（i）在两球上的任意恒定磁场和（ii）较高属表面上的强恒定磁场上的任意恒定磁场的扭曲切线束的Hofer-Zehnder能力。在$ s^2 $上，我们进一步给出了一个明确的$ \ text {so}（3）$ - 扭曲的切线捆绑包至$ s^2 \ times s^2 $，并带有拆分符号形式。前者是在恒定磁场中移动的带电粒子的相位空间，后者是两个无质量耦合的角动量的构型空间。
We determine the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces for (i) arbitrary constant magnetic fields on the two-sphere and (ii) strong constant magnetic fields for higher genus surfaces. On $S^2$ we further give an explicit $\text{SO}(3)$-equivariant compactification of the twisted tangent bundle to $S^2\times S^2$ with split symplectic form. The former is the phase space of a charged particle moving on the two-sphere in a constant magnetic field, the latter is the configuration space of two massless coupled angular momenta.
