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

0203760Balachandran美国-墨西哥奖将支持雪城大学的A.P. Balachandran博士和R.D. Sorkin博士以及阿拉巴马大学的A.B. Stern博士与墨西哥墨西哥城研究中心（CINVESTAV）的D. O'Connor博士和R. Capovilla博士进行研究合作。研究人员打算在非交换几何的一般领域中研究各种各样的想法，这些想法在量子物理、弦理论和相对论中有重要的应用。国际科学与工程办公室和美国国家科学基金会物理部将为这项研究提供资金。这个项目有两个组成部分。第一个是利用非交换几何的新思想发展一种替代格场理论的方法。该方法使用矩阵代数来近似空间的函数代数，随着矩阵变大，近似变得更精细。该方法具有保留了基本的手性和超对称性以及易于捕获拓扑数据的优点。该部分还包含了对非交换空间的场论的更完整的研究，特别强调了非交换的chen - simons理论。第二个部分涉及量子引力的因果集方法，其中量子时空从离散的因果结构中出现。项目这方面的主要目标是为因果集找到合适的量子顺序增长动力学。该项目的两个组成部分都有一个重要的数值组成部分，目前处于校准阶段的第一个组成部分的蒙特卡罗模拟。数字工作由墨西哥小组进行，他们是所涉及的统计物理学方面的专家，而美国小组则是该项目的代数和拓扑学方面的专家。

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.