Theoretical Studies of Quantum Systems with Strong Interactions

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9509533 Wiegmann Theoretical research will be conducted on nonperturbative problems in quantum field theory and condensed matter physics. In particular, electronic systems with strong interactions and topological fluids will be studied. Topics to be studied include Fermi and Bose systems with vector gauge interactions which describe the Mott insulator, liquid state of flux lines in superconductors, fractional quantum Hall effect, and topological liquids. The research will focus on topological effects of the gauge field, the character of the ground state of the gauged system, toplogical instability, and fractionalization of the spectrum as a result of a quantum phase transition. %%% A variety of physical systems will be investigated which are of current interest. All of these systems are characterized by the fact that they are strongly interacting and cannot be treated using existing theoretical techniques. The theoretical approach will be a mathematical one using field theoretical techniques. The results of this work will contribute to both condensed matter physics and its mathematical foundations. ***