Theoretical Studies of Anyon Superconductivity

任意子超导性的理论研究——自然界（任意子）中分数统计的出现，分数统计引起超导性的能力，以及分数统计在强相关模型系统（例如，Hubbard和t-J模型）的正式描述中的自然出现，现在已经牢固地建立起来。因此，任何子对都必须被接受为高tc超导的潜在情况。目前尚不清楚是否在这些（或任何）真实材料中确实存在任何离子超导性。这个问题将一直保持开放，直到有足够强大的数学工具能够准确而正确地描述任何粒子效应。提出的研究包括基于微扰技术的正式程序的发展，以描述现实环境中的任意离子超导性，以及使用这些程序计算高tc材料的光谱特性。这项工作的目的是建立一个精确的任意子超导的图像，也就是说，超导的基本对象是奇分数自旋实体对，而不是产生正常超导现象的成对电子。这种新形式的超导性本身很重要，但也是最近发现的高tc超导现象的合理模型。本工作的中心特点是适合于详细讨论这一现象的数学机制的发展和应用。

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.