Geometric Phases in Classical and Quantum Mechanics

Presents basic mathematical tools on manifolds and differential forms. This book explains topological invariants (Chern classes and homotopy theory) with emphasis on physical applications. It is suitable for physicists and graduate students in physics for learning techniques of differential geometry in an applied context.

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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.