Quantum Holonomy and its Application

关于量子绝热相的具体特征，我们得到了以下结果。(1)对原子核的旋转-粒子耦合模型进行了绝热相效应的定量估计。(2)：针对非阿贝尔规范场中绝热相与手性异常之间的关系，将规范变换发生器的反常换向子表述为规范场相关辛结构的变形。(3)：超对称（SUSY）量子力学是WKP理论包括绝热相的一个显著结果。(4)：作为绝热相在凝聚态物理中的应用，我们考察了绝热相对多粒子模型平均场理论的影响。其中，(i) BCS超导模型，我们推导出铜对的电荷变为分数。（ii）莫特绝缘体，由于绝热相的影响，描述粒子空穴凝聚的序参量模式所携带的量子数变为分数。(5)：将He^3超流体输运系数的拓扑量子化推测为伴随序参量相位绝热变化的相完整效应，可视为与量子霍尔效应的直接类比。(6)：利用广义相干态，将绝热相的概念推广为“典型相”的概念。

We have obtained the following results on the specific features of the quantum adiabatic phase.(1): A quantitative estimate of the effect of the adiabatic phase has been carried out for the rotational-particle coupling model of nuclei.(2): Concerning the connection between the adiabatic phase and the chiral anomaly in non-abelian gauge field, the anomalous commutators for the generators of gauge transformation is formulated as the deformation of the symplectic structure associated with the gauge field.(3): The supersymmetric (SUSY) quantum mechanics has been obtained as a remarkable consequence of the WKP theory including the adiabatic phase.(4): As applications of the adiabatic phase to condensed matter physics, we have examined the effect on the mean field theory of many-particle models. Among others, (i) the BCS superconductivity model, for which we deduce that the charge of the cooper pair becomes fractional. (ii) the Mott insulator, for which the quantum number carried by the mode of order parameter describing the particlehole condensate becomes fractional as an effect of the adiabatic phase.(5): The topological quantization of the transport coefficient in superfluid He^3 is conjectured as an effect of the phase holonomy accompany in the adiabatic change of the order parameter phase, which can be regarded as a direct analogy with the quantum Hall effect.(6): The concept of "canonical phase" is formulated as a generalization of the adiabatic phase by using the generalized coherent state.