عنوان

Geometric Phases in Classical and Quantum Mechanics

شابک

9780817681760

شابک

9781461264750

شماره

b402579

عنوان اصلي

Geometric Phases in Classical and Quantum Mechanics

نام عام مواد

[Book]

نام نخستين پديدآور

by Dariusz Chruściński, Andrzej Jamiołkowski.

محل نشرو پخش و غیره

Boston, MA :

نام ناشر، پخش کننده و غيره

Imprint: Birkhäuser,

تاریخ نشرو بخش و غیره

2004.

عنوان فروست

Progress in Mathematical Physics ;

مشخصه جلد

36

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9781461264750

عنوان

Springer eBooks

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

Mathematical physics.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Mechanics.

موضوع مستند نشده

Quantum theory.

موضوع مستند نشده

Topological Groups.

مستند نام اشخاص تاييد نشده

Chruściński, Dariusz.

مستند نام اشخاص تاييد نشده

Jamiołkowski, Andrzej.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301082600.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y