论文标题
全态哈密顿系统的真实形式
Real Forms of Holomorphic Hamiltonian Systems
论文作者
论文摘要
通过使哈密顿系统复杂化，可以在全体形态符号歧管上获得动力学。为了倒转这种结构，我们提出了一种真实形式的理论，该理论不仅恢复了原始系统，而且产生了具有相同络合力的不同真实的哈密顿系统。这为霍米尔顿系统的真实形式提供了一种类似于复杂谎言代数的真实形式的系统的概念。我们的主要结果是，在硕士上，任何分析机械系统的复杂化都在紧凑的符号歧管上承认了一种真实形式。这为哈密顿系统产生了一个“统一技巧”，奇怪地需要对Hyperkähler几何形状进行必不可少的使用。我们通过为简单的摆，球形摆和刚体的身体找到紧凑的真实形式来证明这一结果。
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real Hamiltonian systems which share the same complexification. This provides a notion of real forms for holomorphic Hamiltonian systems analogous to that of real forms for complex Lie algebras. Our main result is that the complexification of any analytic mechanical system on a Grassmannian admits a real form on a compact symplectic manifold. This produces a `unitary trick' for Hamiltonian systems which curiously requires an essential use of hyperkähler geometry. We demonstrate this result by finding compact real forms for the simple pendulum, the spherical pendulum, and the rigid body.
