量子演化中的球面流形
Spherical Manifold in Quantum Evolution
摘要：
本文利用射影几何描述了量子演化中球流形的性质和离散性。当系统随时间演化时，状态向量会改变，并在希尔伯特空间中描绘出一条曲线。在几何上，演化被表示为投影希尔伯特空间中的闭合曲线。在最近的时代已经作出了许多尝试来描述“长度”，“距离”，和“几何相位”，也“平行运输”和辛几何在各种方式在投影希尔伯特空间，在量子演化。本文证明了光线空间中的量子演化，球流形和离散性特征可以用几何方法描述。
英文摘要：
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space. Geometrically, the evolution is represented as a closed curve in the projective Hilbert space. In recent times many attempts have been made to describe 'length', 'distance', and 'geometric phases' and also 'parallel transport'and symplectic geometry in various ways in the projective Hilbert space, during quantum evolution. It is shown in this paper that for the quantum evolution in ray space, spherical manifold and features of discreteness can be described geometrically.
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