Gauge-independent formalism for parallel transport, geodesics and geometric phase
Gauge-independent formalism for parallel transport, geodesics and geometric phase
复制标题
平行传输、测地线和几何相位的与规范无关的形式主义
DOI：
10.1088/0305-4470/32/27/314
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
V. C. Rakhecha
中科院分区：
文献类型：
--
作者：
A. G. Wagh;V. C. Rakhecha
对于一般的量子系统，导出了一对密度算符之间的有限差分的物理性质，并得到了相应的2-子空间的完备生成元集。任何一般射线空间演化中的每一个无限小的步骤都发生在局部2-子空间中，并且可以等同于等效自旋-1/2粒子的“自旋”旋转。因此，实现给定射线空间演化的完全一般的哈密顿算子包括局部2-子空间中的泡利算子，使用给定的密度算子及其微分构造。动态相位与旋转参考系中的相位相同，在该旋转参考系中，“自旋”保持静止。从旋转坐标系到实验室坐标系的转换影响了平行输运演化，产生几何相位。导出了测地线的密度算子方程。几何相位产生于局部“自旋”的平行输运，等于2-子空间立体角积分的负一半。
For a general quantal system, physical properties of the finite difference between a pair of density operators are derived and a complete set of generators for the associated 2-subspace is obtained. Each infinitesimal step in any general ray-space evolution takes place in the local 2-subspace and can be equated to a `spin' rotation for the equivalent spin-½ particle. Hence a completely general Hamiltonian implementing a given ray space evolution comprises Pauli operators in the local 2-subspaces, constructed using the given density operator and its differential. Dynamical phase identifies with the phase in a rotating reference frame in which the `spin' remains stationary. The transformation from this rotating frame to the laboratory frame effects a parallel transport evolution, producing geometric phase. A density operator equation is derived for geodesics. Geometric phase arises from the parallel transport of the local `spin' and equals minus half the integral of 2-subspace solid angles.