Geometric Phases in Classical and Quantum Mechanics [Paperback]

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

Introduction * 0. PRELIMINARY MATHEMATICAL BACKGROUND * I. THE ADIABATIC PHASE * 1. The Adiabatic Phase in Quantum Mechanics * 2. The Adiabatic Phase in Classical Mechanics * 3. Adiabatic phase and holonomy * II. DIFFERENTIAL GEOMETRY AND THE GEOMETRIC PHASE * 4. Geometry of a sphere and the geometric phase * III. THE GEOMETRY OF QUANTUM EVOLUTION * 5. The Aharonov--Anandan phase * 6. Geometric phase for a non-cyclic evolution * IV. EXAMPLES AND APPLICATIONS * 7.Harmonic oscillator * 8. Geometric phase in optics * 9. Geometric phase in molecular systems * 10. Geometric phase and the motion in noninertial frames * Mathematical Appendices * References * Index

This monograph is the most recent addition to the body of book length surveys on the topic of geometric phases and physics addressed primarily to physicists...the present title is a most welcome and useful addition. The entire text is very clearly written, well-organized, and generously interspersed with examples (both mathematical and physical) illustrating the abstract formulations. The writing style is efficiently pedagogical and concise, with just the right amount of detail to avoid confusion and repetition in what is after all a very complex, intricate and difficult topic. ---Mathematical Reviews

The book under review provides a unified treatment of geometric phases in quantum and classical mechanics, which is mainly based on fiber bundle theory...[T]his is a nice and well-ló!