Geometric Phases in Classical and Quantum Mechanics (Progress in Mathematical Physics) (Hardcover)

by Dariusz Chruscinski (Author), Andrzej Jamiolkowski (Author) "The concept of a manifold generalizes the concept of a smooth surface or a curve in R3..." (more)
Key Phrases: transported basis, spectral bundle, monopole bundle, General Relativity, Kato Hamiltonian (more...)

Editorial Reviews

Review
"This monograph is the most recent addition to the body of book length surveys on the topic of geometric phases and physics addressed primarily to physicists...the present title is a most welcome and useful addition. The entire text is very clearly written, well-organized, and generously interspersed with examples (both mathematical and physical) illustrating the abstract formulations. The writing style is efficiently pedagogical and concise, with just the right amount of detail to avoid confusion and repetition in what is after all a very complex, intricate and difficult topic." ---Mathematical Reviews "The book under review provides a unified treatment of geometric phases in quantum and classical mechanics, which is mainly based on fiber bundle theory...[T]his is a nice and well-written book about an interesting subject. It can be recommended to students and researchers in mathematics and theoretical physics with interests in geometric structures of theoretical physics and with sufficient knowledge about differential geometry." ---Zentralblatt MATH "The book forms a compact, yet comprehensive, introduction to the mathematical physics of this young field.... Its large bibliography should serve as a quick reference to the relevant literature. Mathematical appendices have been thoughtfully provided for students. Suggested references for further reading and illustrative exercises listed at the end of each chapter are useful to gain a better understanding of the respective topic.... All in all, this is a good textbook ushering the graduate student through the wonderland of geometric phase and whetting up the appetite for further exploration." —Current Science "This new textbook examines one of the most interesting findings of the last several decades–the physical importance of the topological and geometrical phases in classical and quantum mechanics.... The number of research publications on this topic has grown at such a pace that, for non-experts, it has become difficult to follow the numerous theoretical ideas and experimental proposals that have been presented.... What distinguishes the present book...is that it treats both the quantum and classical geometric phases from a unified (fibre bundle connection) point of view at an advanced textbook level.... Every chapter contains illustrative problems and an annotated list of references for further reading.... The book is well written and...the choice of topics presented and their mathematical description and physical explanation are well balanced and appropriate. The book is aimed mainly at graduate students in mathematics and theoretical physics. It would, however, also be useful to (young and mature) researchers in different fields of theoretical physics and chemistry who want to familiarize themselves with modern differential geometry methods and techniques, and to mathematicians who wish to learn about a class of applications of the above methods in classical and quantum theory." —Journal of Geometry and Symmetry in Physics

Product Description
Several well-established geometric and topological methods are used in this work on a beautiful and important physical phenomenon known as the 'geometric phase.' Going back to the intense interest in this subject since the mid-1980s and the seminal work of M. Berry and B. Simon, this book examines geometric phases, bringing together different physical phenomena under a unified mathematical scheme. Key background material, beginning with the notion of manifolds and differential forms, as well as basic mathematical tools -- fiber bundles, connections and holonomies -- are presented in Chapter 1. Topological invariants such as Chern classes and homotopy theory are explained in simple, concrete language with emphasis on physical applications. The exposition then unfolds systematically. The adiabatic phases of Berry, the Wilczek--Zee nonabelian factor, and a classical counterpart called Hannay's angles focus on the physical side of the geometric phase problem. Thereafter the geometry of quantum evolution is treated. Here the reader learns about different geometries (such as symplectic and metric structures) living on a quantum phase space in connection with both abelian and nonabelian geometric phases. The concluding section on Examples and Applications paves the way for a continuing study of the geometric PHASES. Throughout the text, material is presented on a level suitable for graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics.

Product Details

• Hardcover: 344 pages
• Publisher: Birkhäuser Boston; 1 edition (June 15, 2004)
• Language: English
• ISBN-10: 081764282X
• ISBN-13: 978-0817642822
• Product Dimensions: 9.3 x 6.3 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: No customer reviews yet. Be the first.
• Amazon.com Sales Rank: #993,911 in Books (See Bestsellers in Books)