论文标题
氦气中冷冻行星轨道的非修饰和整体数量
Nondegeneracy and integral count of frozen planet orbits in helium
论文作者
论文摘要
我们研究了一个作用功能家族的临界点在冷冻的行星轨道之间的临界点在氦气原子中，电子与自由下落之间的平均相互作用。本文相当令人惊讶的第一个结果断言，对于整个家庭来说，关键点总是不化的。这意味着具有平均相互作用的冷冻行星轨道是非排定的，并给出了其独特性的新证明。作为一种应用，我们表明，瞬时相互作用的冷冻行星轨道的积分计数等于一个。为此，我们证明了根据Selfadexhoint Fredholm Operators的空间范围内的SelfAdaint Line Bundle的可定位性，并使用它来定义弗雷德霍尔姆（Fredholm）截面的整数有价值的欧拉（Euler）特征，其线性化属于该类别。
We study a family of action functionals whose critical points interpolate between frozen planet orbits for the helium atom with mean interaction between the electrons and the free fall. The rather surprising first result of this paper asserts that for the whole family, critical points are always nondegenerate. This implies that the frozen planet orbit with mean interaction is nondegenerate and gives a new proof of its uniqueness. As an application, we show that the integral count of frozen planet orbits with instantaneous interaction equals one. For this, we prove orientability of the determinant line bundle over the space of selfadjoint Fredholm operators with spectrum bounded from below, and use it to define an integer valued Euler characteristic for Fredholm sections whose linearization belongs to this class.
