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Catalogue Information
Field name	Details
Dewey Class	519
Title	Geometric Phases in Classical and Quantum Mechanics ([EBook] /) / by Dariusz Chruściński, Andrzej Jamiołkowski.
Author	Chruściński, Dariusz
Added Personal Name	Jamiołkowski, Andrzej author.
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : : Birkhäuser Boston : : Imprint: Birkhäuser, , 2004.
Physical Details	XIII, 337 p. : online resource.
Series	Progress in Mathematical Physics ; 36
ISBN	9780817681760
Summary Note	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. .:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-8176-0
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Differential Geometry . Engineering mathematics . Lie groups . Mathematical Methods in Physics . Mathematics . Mechanics . Physics . Quantum Physics . Topological groups . Topological groups, Lie groups . Authors: Chruściński, Dariusz . Jamiołkowski, Andrzej . Corporate Authors: SpringerLink (Online service) . Series: Progress in Mathematical Physics . Classification: 519 .

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Geometric Phases in Classical and Quantum Mechanics

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