<電子ブック>
Geometric Phases in Classical and Quantum Mechanics / by Dariusz Chruscinski, Andrzej Jamiolkowski
(Progress in Mathematical Physics. ISSN:21971846 ; 36)
版 | 1st ed. 2004. |
---|---|
出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 2004 |
本文言語 | 英語 |
大きさ | XIII, 337 p : online resource |
著者標目 | *Chruscinski, Dariusz author Jamiolkowski, Andrzej author SpringerLink (Online service) |
件 名 | LCSH:Mathematics LCSH:Topological groups LCSH:Lie groups LCSH:Geometry, Differential LCSH:Quantum physics LCSH:Mathematical physics LCSH:Mechanics FREE:Applications of Mathematics FREE:Topological Groups and Lie Groups FREE:Differential Geometry FREE:Quantum Physics FREE:Mathematical Methods in Physics FREE:Classical Mechanics |
一般注記 | 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 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. HTTP:URL=https://doi.org/10.1007/978-0-8176-8176-0 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9780817681760 |
|
電子リソース |
|
EB00231145 |
類似資料
この資料の利用統計
このページへのアクセス回数:8回
※2017年9月4日以降