{"product_id":"geometric-phases-in-classical-and-quantum-mechanics-9781461264750","title":"Geometric Phases in Classical and Quantum Mechanics","description":"\u003cp\u003e • Author(s): Dariusz Chruscinski\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Applied\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eSeveral 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. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eKey Topics and Features: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Background material presents basic mathematical tools on manifolds and differential forms. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Topological invariants (Chern classes and homotopy theory) are explained in simple and concrete language, with emphasis on physical applications. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Berry's adiabatic phase and its generalization are introduced. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- 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. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Quantum mechanics is presented as classical Hamiltonian dynamics on a projective Hilbert space. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Hannay's classical adiabatic phase and angles are explained.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Review of Berry and Robbins' revolutionary approach to spin-statistics. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- A chapter on Examples and Applications paves the way for ongoing studies of geometric phases. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Problems at the end of each chapter. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e- Extended bibliography and index. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eGraduate 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. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45277271031959,"sku":"9781461264750","price":5876.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781461264750.webp?v=1769287934","url":"https:\/\/atlanticbooks.com\/products\/geometric-phases-in-classical-and-quantum-mechanics-9781461264750","provider":"Atlantic Books","version":"1.0","type":"link"}