复Grassmann流形上的Hamilton系统Holonomy与Schrodinger方程
Hamiltonian Systems on Complex Grassmann Manifold. Holonomy and Schrodinger Equation
摘要：
研究了复Grassmann流形上的正则向量丛的主丛、该丛上的正则联络形式、复Grassmann流形上的正则辛形式以及相应的动力系统等微分几何结构. Grassmann流形被认为是余伴随作用的轨道，辛形式被描述为李余代数上的标准Poisson结构的限制。研究了Hamilton动力系统的积分曲线在Grassmannian上的联络的完整性及其与Berry相的关系。
英文摘要：
Differential geometric structures such as the principal bundle for the canonical vector bundle on a complex Grassmann manifold, the canonical connection form on this bundle, the canonical symplectic form on a complex Grassmann manifold and the corresponding dynamical systems are investigated. The Grassmann manifold is considered as an orbit of the co-adjoint action and the symplectic form is described as the restriction of the canonical Poisson structure on a Lie coalgebra. The holonomy of the connection on the principal bundle over Grassmannian and its relation with Berry phase is considered and investigated for the integral curves of Hamiltonian dynamical systems.
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