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" Geometric Phases in Classical and Quantum Mechanics "
by Dariusz Chruściński, Andrzej Jamiołkowski.
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BL
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573360
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b402579
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| Main Entry
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Chruściński, Dariusz.
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| Title & Author
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Geometric Phases in Classical and Quantum Mechanics\ by Dariusz Chruściński, Andrzej Jamiołkowski.
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| Publication Statement
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Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 2004.
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| Series Statement
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Progress in Mathematical Physics ;; 36
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| ISBN
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9780817681760
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: 9781461264750
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| Contents
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1 Mathematical Background -- 2 Adiabatic Phases in Quantum Mechanics -- 3 Adiabatic Phases in Classical Mechanics -- 4 Geometric Approach to Classical Phases -- 5 Geometry of Quantum Evolution -- 6 Geometric Phases in Action -- A Classical Matrix Lie Groups and Algebras -- B Quaternions.
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| Abstract
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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 graduate students in physics will learn techniques of differential geometry in an applied context.
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Mathematics.
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Topological Groups.
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Global differential geometry.
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Quantum theory.
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Mathematical physics.
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Mechanics.
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Jamiołkowski, Andrzej.
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SpringerLink (Online service)
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