Geometric Phases in Classical and Quantum Mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schriftenreihe: | Progress in Mathematical Physics
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIII, 337 p) |
| ISBN: | 9780817681760 9781461264750 |
| DOI: | 10.1007/978-0-8176-8176-0 |
Internformat
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| 490 | 1 | |a Progress in Mathematical Physics |v 36 | |
| 500 | |a 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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Datensatz im Suchindex
| _version_ | 1804153089533411328 |
|---|---|
| any_adam_object | |
| author | Chruściński, Dariusz |
| author_GND | (DE-588)124199771 (DE-588)140988661 |
| author_facet | Chruściński, Dariusz |
| author_role | aut |
| author_sort | Chruściński, Dariusz |
| author_variant | d c dc |
| building | Verbundindex |
| bvnumber | BV042419194 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184300142 (DE-599)BVBBV042419194 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-8176-0 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817681760 9781461264750 |
| language | English |
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| spelling | Chruściński, Dariusz Verfasser (DE-588)124199771 aut Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruściński, Andrzej Jamiołkowski Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XIII, 337 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematical Physics 36 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 Mathematics Topological Groups Global differential geometry Quantum theory Mathematical physics Mechanics Applications of Mathematics Topological Groups, Lie Groups Differential Geometry Quantum Physics Mathematical Methods in Physics Mathematik Mathematische Physik Quantentheorie Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Berry-Phase (DE-588)4296737-5 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Berry-Phase (DE-588)4296737-5 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Jamiołkowski, Andrzej 1946- Sonstige (DE-588)140988661 oth Progress in Mathematical Physics 36 (DE-604)BV013823265 36 https://doi.org/10.1007/978-0-8176-8176-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chruściński, Dariusz Geometric Phases in Classical and Quantum Mechanics Progress in Mathematical Physics Mathematics Topological Groups Global differential geometry Quantum theory Mathematical physics Mechanics Applications of Mathematics Topological Groups, Lie Groups Differential Geometry Quantum Physics Mathematical Methods in Physics Mathematik Mathematische Physik Quantentheorie Mathematische Physik (DE-588)4037952-8 gnd Quantentheorie (DE-588)4047992-4 gnd Berry-Phase (DE-588)4296737-5 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4047992-4 (DE-588)4296737-5 |
| title | Geometric Phases in Classical and Quantum Mechanics |
| title_auth | Geometric Phases in Classical and Quantum Mechanics |
| title_exact_search | Geometric Phases in Classical and Quantum Mechanics |
| title_full | Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruściński, Andrzej Jamiołkowski |
| title_fullStr | Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruściński, Andrzej Jamiołkowski |
| title_full_unstemmed | Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruściński, Andrzej Jamiołkowski |
| title_short | Geometric Phases in Classical and Quantum Mechanics |
| title_sort | geometric phases in classical and quantum mechanics |
| topic | Mathematics Topological Groups Global differential geometry Quantum theory Mathematical physics Mechanics Applications of Mathematics Topological Groups, Lie Groups Differential Geometry Quantum Physics Mathematical Methods in Physics Mathematik Mathematische Physik Quantentheorie Mathematische Physik (DE-588)4037952-8 gnd Quantentheorie (DE-588)4047992-4 gnd Berry-Phase (DE-588)4296737-5 gnd |
| topic_facet | Mathematics Topological Groups Global differential geometry Quantum theory Mathematical physics Mechanics Applications of Mathematics Topological Groups, Lie Groups Differential Geometry Quantum Physics Mathematical Methods in Physics Mathematik Mathematische Physik Quantentheorie Berry-Phase |
| url | https://doi.org/10.1007/978-0-8176-8176-0 |
| volume_link | (DE-604)BV013823265 |
| work_keys_str_mv | AT chruscinskidariusz geometricphasesinclassicalandquantummechanics AT jamiołkowskiandrzej geometricphasesinclassicalandquantummechanics |