几何相位与隐规范对称性
Geometric phases and hidden gauge symmetry
摘要：
第二个几何相位的量化方法进行审查。第二量子化通常会导致一个隐藏的局部（含时）规范对称性。这种规范对称性定义了平行输运和完整性，因此它以统一的方式控制了所有已知的几何相，无论是绝热的还是非绝热的。从绝热到非绝热相的过渡区，从而在定量的方式进行了分析。然后，它示出的绝热Berry相的拓扑结构是平凡的，在一个精确的意义上，也是绝热相是相当脆弱的对非绝热变形。在这个公式中，像投影希尔伯特空间这样的概念并没有出现。
英文摘要：
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls all the known geometric phases, either adiabatic or non-adiabatic, in a unified manner. The transitional region from the adiabatic to non-adiabatic phases is thus analyzed in a quantitative way. It is then shown that the topology of the adiabatic Berry's phase is trivial in a precise sense and also the adiabatic phase is rather fragile against the non-adiabatic deformation. In this formulation, the notion such as the projective Hilbert space does not appear.
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