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

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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.