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Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruscinski

Geometric Phases in Classical and Quantum Mechanics

by Dariusz Chruscinski
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Book cover type: Paperback
  • ISBN13: 9781461264750
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 337
  • Original Price: EUR 79.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 537 grams
  • BISAC Subject(s): Applied, Physics / Quantum Theory, and Group Theory

From the Back Cover

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 graduate students in physics will learn techniques of differential geometry in an applied context.

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