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.
