Applications of functional bosonization and infinite-dimensional gauge theories to the study of quantum transport phenomena

从量子霍尔系统中Skyrmion激发的观察可以看出，低维电子系统提供了一个现实的地方来测试和应用规范理论的各种想法和技术。在过去三年的资助下，我们研究了分数量子霍尔效应的各个方面，如复合玻色子/费米子，集体激发和双层系统中的层间相干性，以及作为一个新的学科，超对称性和拓扑激发的相互作用。结合单模近似和W_∞代数的非线性实现，我们建立了一个基于量子Hall态不可压缩性质的长波有效的双折射理论，而不涉及双折射的标准复合玻色子或复合费米子图像。我们应用它来研究，特别是，在双层霍尔系统中固有的集体激发的一些特征。在某些超对称理论中，拓扑（或中心）电荷获得了一种新型的量子反常，它在拓扑激发的存在下起着重要的作用。在2003年的学术论文中，我提出了一个孤立子中心电荷异常的超场公式，并讨论了它们的起源和作用。我在2004年的学术研讨会上将超空间分析扩展到了畴壁和涡旋。超空间方法告诉我们，中心电荷异常的问题本质上是超电流的超迹问题，并揭示了这些异常的对偶（玻色子/费米子）特征。

As seen from the observation of Skyrmion excitations in quantum Hall systems, low-dimensional electron systems offer a realistic place to test and apply various ideas and techniques of gauge theories. Under a Grant-in-Aid over the past three years we have studied various aspects of the fractional quantum Hall effect (FQHE), such as composite bosons/fermions, collective excitations, and inter-layer coherence in bilayer systems, and, as a new subject, an interplay of supersymmetry and topological excitations.1. Combined use of the single-mode approximation and nonlinear realization of the W_∞ algebra enabled us to construct a long-wavelength effective theory of the FQHE, that relies on the incompressible nature of the quantum Hall states without referring to the standard composite-boson or composite-fermion picture of the FQHE. We applied it to study, in particular, some characteristic features of the collective excitations inherent in bilayer Hall systems.2. In certain supersymmetric theories topological (or central) charges acquire a new type of quantum anomalies, which play an important role in the presence of topological excitations. In academic 2003 I developed a superfield formulation of the central-charge anomalies for solitons and discussed their origins and role. I extended a superspace analysis to domain walls and vortices during academic 2004. The superspace approach tells us that the problem of central-charge anomalies is essentially the problem of the supertrace of the supercurrent, and reveals a dual (bosonic/fermionic) character of these anomalies.