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

0203760 Balachandran美国-墨西哥奖将支持A. P. Balachandran博士和R.D.博士。锡拉丘兹大学的索尔金和A.B.亚拉巴马大学的斯特恩博士与D.奥康纳和R. Capovilla的Centro de Investigacion y de Estudios Avanzados del IPN（CINVESTAV）在墨西哥城，墨西哥. 研究人员打算在非对易几何的一般领域研究各种想法，并将其应用于量子物理学，弦理论和相对论。 美国国家科学基金会国际科学与工程办公室和物理部将为这项研究提供资金。 第一个是发展一种替代格场理论使用新兴的想法从非交换几何。 该方法使用矩阵代数来近似空间的函数代数，随着矩阵变得更大，近似变得更精细。该方法具有保持基本对称性（包括手征和超对称性）和易于捕获拓扑数据的优点。 这一部分还包括对非对易空间场论的更完整的研究，特别强调非对易陈-西蒙斯理论。 第二部分涉及因果集方法的量子引力，量子时空出现从一个离散的因果结构。该项目这方面的主要目标是为因果集找到合适的量子序贯增长动力学。该项目的两个组成部分都有一个重要的数字组成部分，目前在校准阶段的第一个组成部分的蒙特卡罗模拟。数值计算工作由墨西哥小组进行，他们是所涉统计物理学方面的专家，而美国同行则是该项目代数和拓扑方面的专家。

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.