Geometric phases and hidden local gauge symmetry
Geometric phases and hidden local gauge symmetry
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DOI：
10.1103/physrevd.72.025009
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发表时间：
2005-05
影响因子：
5
通讯作者：
K. Fujikawa
中科院分区：
文献类型：
--
作者：
K. Fujikawa
与能级交叉相关的几何相位的分析减少到熟悉的对角化的哈密顿量的第二个量化的配方。一个隐藏的局部规范对称性，这是与一个完整的正交基组的相位选择的任意性，成为明确的在这个公式（特别是在绝热近似），并指定物理可观的。在第二量子化中，指定函数空间中坐标的基组的选择是任意的，并且保持作用形式不变的坐标变换的子类被认为是规范对称性。我们详细讨论了这种隐藏的局部规范对称性的影响，通过分析几何相位循环和非循环演化。它表明，隐藏的局部对称性提供了一个基本的概念替代的概念，holonomy来分析几何相位和分析的基础上隐藏的局部规范对称性导致的结果符合一般规定的Pancharatnam。然而，我们注意到循环和非循环演化的几何相位之间的重要差异。我们还解释了隐藏的局域规范对称性与Aharonovmore »和Anandan在广义几何相定义中使用的规范对称性（或等价类）之间的基本区别。«少
The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a subclass of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonovmore » and Anandan in their definition of generalized geometric phases.« less