U.S.-Western Europe Cooperative Science: The Geometric Phase in Quantum Mechanics

该奖项将支持Jeeva Anandan博士与两位欧洲科学家在理论物理学方面进行合作研究：德意志联邦共和国慕尼黑马克斯·普朗克物理与天体物理研究所Leo Stodolsky教授和英国剑桥大学应用数学与理论物理系Garry Gibbons教授。几何思想在物理学中的重要性怎么强调都不为过。例如，闵可夫斯基对狭义相对论的几何重新表述，使爱因斯坦能够创立一种新的引力相对论，即广义相对论。近年来，在量子理论中发现了一个新的几何概念，它不依赖于时空或规范场几何，只依赖于希尔伯特空间内积。这是从贝里发现不可积相位因子开始的。尽管自Berry的开创性工作以来，已经有数百篇关于几何相位的论文，但仍有许多深刻的基本问题未得到解答，Anandan博士建议在拟议的研究期间对其进行调查。这些问题涉及1)几何相的协变公式2)海森堡图中的公式3)几何相的不变公式4)富比尼-研究度量的实验观察5)二阶时间方程的几何相6)非阿贝尔几何相的经典模拟7)与引力相的联系以及8)物理应用。在马克斯·普朗克物理和天体物理研究所，阿南丹博士将与斯托尔斯基博士一起研究几何相位和带电粒子干涉测量的一种新的相对论性引力效应。在剑桥大学，他将继续和吉本斯博士一起研究非绝热几何相。这一研究结果将对理解量子力学中的几何相作出重要贡献。

This award will support Dr. Jeeva Anandan to carry out collaborative research in theoretical physics with two European scientists: Professor Leo Stodolsky, Max Planck Institute for Physics and Astrophysics, Munich, Federal Republic of Germany and Professor Garry Gibbons, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England. The importance of geometric ideas in physics cannot be over emphasized. The geometrical reformulation of special relativity by Minkowski, for example, enabled Einstein to create a new relativistic theory of gravitation, namely general relativity. Recently, a new geometric concept was discovered in quantum theory, which is independent of space-time or gauge field geometries and depends on the Hilbert space inner product only. This began with the discovery of a nonintegrable phase factor by Berry. Although hundreds of papers have been written on the geometric phase, since the pioneering work of Berry, there are still a number of deep fundamental unanswered questions, which Dr. Anandan proposals to investigate during the period of proposed research. These questions concern 1) covariant formulation of the geometric phase 2) formulation in the Heisenberg picture 3) invariant formulation of the geometric phase 4) experimental observation of the Fubini-Study metric 5) geometric phase for equations that are second order in time 6) the classical analog of the non abelian geometric phase 7) connection to the gravitational phase and 8) physical applications. At the Max Planck Institute for Physics and Astrophysics, Dr. Anandan will work with Dr. Stodolsky on both the geometric phase and on a new relativistic gravitational effect on charged particle interferometry. At Cambridge University he will continue to study with Dr. Gibbons the non adiabatic geometric phase. The results of this research should make an important contribution to the understanding of the geometric phase in quantum mechanics.