Geometric Phases in Classical and Quantum Mechanics / Progress in Mathematical Physics Bd.36 (PDF)
This work examines the beautiful and important physical concept known as the 'geometric phase,' bringing together different physical phenomena under a unified mathematical and physical scheme.
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This work examines the beautiful and important physical concept known as the 'geometric phase,' bringing together different physical phenomena under a unified mathematical and physical scheme.
Several well-established geometric and topological methods underscore the mathematical treatment of the subject, emphasizing a coherent perspective at a rather sophisticated level. What is unique in this text is that both the quantum and classical phases are studied from a geometric point of view, providing valuable insights into their relationship that have not been previously emphasized at the textbook level.
Key Topics and Features:
. Background material presents basic mathematical tools on manifolds and differential forms.
. Topological invariants (Chern classes and homotopy theory) are explained in simple and concrete language, with emphasis on physical applications.
. Berry's adiabatic phase and its generalization are introduced.
. Systematic exposition treats different geometries (e.g., symplectic and metric structures) living on a quantum phase space, in connection with both abelian and nonabelian phases.
. Quantum mechanics is presented as classical Hamiltonian dynamics on a projective Hilbert space.
. Hannay's classical adiabatic phase and angles are explained.
. Review of Berry and Robbins' revolutionary approach to spin-statistics.
. A chapter on Examples and Applications paves the way for ongoing studies of geometric phases.
. Problems at the end of each chapter.
. Extended bibliography and index.
Graduate students in mathematics with some prior knowledge of quantum mechanics will learn about a class of applications of differential geometry and geometric methods in quantum theory. Physicists and graduatestudents in physics will learn techniques of differential geometry in an applied context.
- Autoren: Dariusz Chruscinski , Andrzej Jamiolkowski
- 2012, 2004, 337 Seiten, Englisch
- Verlag: Birkhäuser Boston
- ISBN-10: 0817681760
- ISBN-13: 9780817681760
- Erscheinungsdatum: 06.12.2012
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- Dateiformat: PDF
- Grösse: 22 MB
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