U.S.- Mexico Cooperative Research: Quantum and Fluctuating Geometries

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0203760BalachandranThis U.S.-Mexico award will support Dr. A.P. Balachandran and Dr. R.D. Sorkin of Syracuse University together with Dr. A.B. Stern of the University of Alabama in a research collaboration with Dr. D. O'Connor and Dr. R. Capovilla of the Centro de Investigacion y de Estudios Avanzados del IPN (CINVESTAV) in Mexico City, Mexico. The researchers intend to work on various ideas in the general area of non-commutative geometry with important applications to quantum physics, string theory, and relativity theory. The Office of International Science and Engineering and the Physics Division of NSF will contribute funds for the research.This project has two components. The first is to develop an alternative to lattice field theory using emerging ideas from non-commutative geometry. The approach uses matrix algebras that approximate the algebra of functions of a space with the approximation becoming finer as the matrices become larger. The method has the advantage of preserving the underlying symmetries including chiral and supersymmetry and easily capturing topological data. This component also incorporates the more complete study of field theories on non-commutative spaces, with particular emphasis on the noncommutative Chern-Simons theory. The second component involves the causal set approach to quantum gravity where the quantum spacetime emerges from a discrete causal structure. The principal goal of this aspect of the project is to find a suitable quantum sequential growth dynamics for causal sets. Both components of the project have a significant numerical component with Monte Carlo simulations for the first component currently in the calibration stage. The numerical work is being carried out by the Mexican group, who are experts in the statistical physics involved, while the US counterparts are experts in the algebraic and topological aspects of the project.