Theoretical Studies of Anyon Superconductivity

对任意子超导电性的理论研究--自然界(任意子)中分数统计的出现，分数统计导致超导的能力，以及在强关联模型系统(例如，Hubbard和t-J模型)的形式描述中分数统计的自然出现，现在已经牢固地建立起来。因此，必须接受任意子配对作为高T_c超导的潜在情况。目前尚不清楚这些(或任何)真实材料中是否真的存在任意子超导性。这个问题将一直悬而未决，直到开发出足够强大的数学工具来准确和正确地描述任意子效应。建议的研究既包括基于微扰技术的形式程序的发展，以描述现实环境中的任意子超导，也包括使用这些程序来计算高T_c材料的光谱性质。这项工作旨在给出一幅准确的任意子超导电性的图景，也就是说，超导电性的基本对象是成对的奇分自旋实体，而不是产生正常超导现象的成对电子。这种新的超导形式本身很重要，但也是最近发现的高温超导现象的一个合理的模型。这项工作的主要特点是发展和应用适合于详细讨论这一现象的数学机器。

Theoretical Studies of Anyon Superconductivity - The occurrence of fractional statistics in nature (anyons)-, the capacity of fractional statistics to cause superconductivity, and the natural appearance of fractional statistics in formal descriptions of strongly correlated model systems (e.g., the Hubbard and t-J models) are now firmly established. As a result, anyon pairing must be accepted as a potential case for high-Tc superconductivity. As yet unclear is whether anyonic superconductivity actually occurs in these (or indeed any) real materials. This question will remain open until mathematical tools sufficiently powerful to describe anyonic effects both accurately and correctly are developed. The proposed research includes both the development of formal procedures, based on perturbative techniques, to describe anyonic superconductivity in realistic settings, and the use of these procedures for computation of spectroscopic properties of high-Tc materials. %%% This work is intended to develop an accurate picture of anyonic superconductivity, that is, superconductivity whose elementary objects are pairs of odd-fractioned spin entities, rather than the paired electrons which produce normal superconductive phenomena. This new form of superconductivity is important in itself, but is also a plausible model for the recently-discovered phenomenon of high-Tc superconductivity. The central feature of the present work is the development and application of mathematical machinery suitable for detailed discussion of this phenomenon.