THREE ELABORATIONS ON BERRY’S CONNECTION, CURVATURE AND PHASE
THREE ELABORATIONS ON BERRY’S CONNECTION, CURVATURE AND PHASE
复制标题
DOI：
10.1142/s0217751x88000114
复制
发表时间：
1988-02
影响因子：
1.6
通讯作者：
R. Jackiw
中科院分区：
文献类型：
--
作者：
R. Jackiw
我们讨论了当贝里相发生在量子系统中时对称性和守恒定律如何受到影响：坐标的对称变换必须由贝里连接的规范变换来补充，因此运动常数获得了超出熟悉的运动学项的项。我们展示了问题的对称性如何决定 Berry 的连接、曲率，以及一旦选择了特定路径，也决定了相位。此外，高阶修正也是固定的。我们证明，在某些情况下，贝里的曲率和相位可以通过全局明确定义的、与时间相关的规范变换来消除。最后，我们描述了如何将场论异常视为贝里相的表现。
We discuss how symmetries and conservation laws are affected when Berry’s phase occurs in a quantum system: symmetry transformations of coordinates have to be supplemented by gauge transformations of Berry’s connection, and consequently constants of motion acquire terms beyond the familiar kinematical ones. We show how symmetries of a problem determine Berry’s connection, curvature and, once a specific path is chosen, the phase as well. Moreover, higher order corrections are also fixed. We demonstrate that in some instances Berry’s curvature and phase can be removed by a globally well-defined, time-dependent canonical transformation. Finally, we describe how field theoretic anomalies may be viewed as manifestations of Berry’s phase.