Elementary Particle Theory

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"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."The goal of this project is to further the understanding of several outstanding contemporary problems in theoretical physics. These problems have originated in worldwide intensive research related to supersymmetric quantum mechanical systems, in general, and to string theory, in particular. A large class of important problems concerning the symmetries of superstring theories and noncommutative geometry will be studied. The proposed activity suggests and explores very creative and original concepts, involving: mathematical deformations and non-commutative geometries in quantum mechanics; Landau levels on super-manifolds and super-coset spaces; quasi-hermitian quantum systems; and N-Lie algebras, with novel applications to conformal field theories and the dynamics of strings and branes. The principle investigators consider these to be important topics with possible novel applications to several physical systems. The broader impacts are as follows: The proposed activity is very important to advancing knowledge and understanding within its own field of elementary particle theory, as well as across different fields, since the use of quantum theory to carry out quantitative calculations, and obtain predictions, is ubiquitous in particle theory and all other physical sciences. Teaching young scholars is an integral part of the career responsibilities of the principle investigators, and is fully symbiotic with their research programs and techniques. The work will broaden and strengthen the developing human resource infrastructure for research and education at the University of Miami. The results will be disseminated broadly in colloquia and seminars, on internet web-pages, on internet archives, and in printed journals, to enhance scientific and technological understanding in its field.