Theorles of Superconductivity and Quantum Hall Effect Via Chem-Simons Gauge Theory.

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Bi-local mean field theory has been applied to strongly correlated electron systems. Especially last year, the vortex solutions of quantum Hall system which are non-linear and topological excitations have been analyzed, and the same method was applied to one dimensional 1/7^2 interacting systems. Main results are the following :(i) Charged vortex solutions and neutral vortex solutions of quantum Hall system are obtained.(ii) Bi-local mean field theory gives a reasonable value to the ground state energy in one dimensional system.(iii) Exponents of correlation functions satisfy the Luttinger liquid relation but are in dis-agreement with those of conformal field theory.