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

该奖项将支持锡拉丘兹大学的A.P.巴拉钱德兰博士和R.D.索尔金博士以及阿拉巴马大学的A.B.斯特恩博士与墨西哥墨西哥城Avanzados del IPN(CINVESTAV)研究中心的D.O‘Connor博士和R.Capovilla博士合作进行研究。研究人员打算在非对易几何的一般领域研究各种想法，并将其重要应用于量子物理、弦理论和相对论。国际科学与工程办公室和国家科学基金会物理部将为这项研究提供资金。该项目由两个部分组成。第一个是利用非对易几何中的新兴思想，开发一种替代格子场理论的方法。该方法使用矩阵代数来逼近空间的函数代数，并且随着矩阵的变大，逼近变得更精细。该方法具有保留手征对称性和超对称性等基本对称性，并易于获取拓扑数据的优点。这一部分还包含了对非对易空间上更完整的场论的研究，特别强调了非对易的Chern-Simons理论。第二个组成部分涉及量子引力的因果集方法，其中量子时空是从离散的因果结构中产生的。该项目这一方面的主要目标是为因果集找到一个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，对目前处于校准阶段的第一个组成部分进行了蒙特卡洛模拟。数值计算工作由墨西哥小组进行，他们是所涉及的统计物理方面的专家，而美国同行则是该项目的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.