Investigations in Field and Particle Theory

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The proposed research involves various aspects of noncommutative physics as well as exactly solvable particle systems and nonperturbative aspects of field theory and gravity. Noncommutative geometry leads to a correspondence between string-membrane quantum theory and fluid dynamical systems. The physical implications of this correspondence will be studied in this research project. The possibility that the quantum Hall system can be described by a non-commutative matrix model will also be investigated. Integrable systems with spin 1 will be investigated in the hope that the anti-ferromagnetic chain continuum limit can be found. The broader implications are the reestablishment of a research environment for undergraduates at Yeshiva University.