Quantum Holonomy and its Application

对于量子绝热相的具体特征，我们得到了如下结果：(1)：对于原子核的转动-粒子耦合模型，对绝热相的影响进行了定量的估计。(2)：关于绝热相与非阿贝尔规范场中手征反常之间的联系，规范变换发生器的反常换向器被表示为与规范场有关的辛结构的形变。(3)：作为包括绝热相在内的WKP理论的显著结果，得到了超对称(SuSY)量子力学。(4)作为绝热相对凝聚态物理的应用，我们得到了超对称(SuSY)量子力学我们考察了它对多粒子模型平均场理论的影响。在其他模型中，(I)BCS超导模型，我们推导出库珀对的电荷是分数的。(2)Mott绝缘体，描述粒子空穴凝聚态的有序参数模式所携带的量子数由于绝热相位的影响而变得分数。(5)：超流He^3输运系数的拓扑量子化是有序参数相位绝热变化伴随的相完整的影响，可视为与量子霍尔效应的直接类比。(6)：利用广义相干态将正则相的概念表述为绝热相位的推广。

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.