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Lie algebras and applications

Author: Francesco Iachello
Publisher: Berlin : Springer, 2015, ©2006.
Series: Lecture notes in physics, v. 891.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical  Read more...
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Additional Physical Format: (GyWOH)har140422620
Document Type: Book
All Authors / Contributors: Francesco Iachello
ISBN: 9783662444931 3662444933 3662444941 9783662444948
OCLC Number: 894847304
Notes: Textbook for graduates.
Description: xviii, 272 pages : illustrations ; 24 cm.
Contents: Basic Concepts --
Semisimple Lie Algebras --
Lie Groups --
Lie Algebras and Lie Groups --
Homogeneous and Symmetric Spaces (Coset Spaces). --
Irreducible Bases (Representations) --
Casimir Operators and Their Eigenvalues --
Tensor Operators --
Boson Realizations --
Fermion Realizations --
Differential Realizations --
Matrix Realizations --
Coset Spaces --
Spectrum Generating Algebras and Dynamic Symmetries --
Degeneracy Algebras and Dynamical Alebras --
Index.
Series Title: Lecture notes in physics, v. 891.
Responsibility: Francesco Iachello.

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"Its intention is to provide an introduction to Lie algebras at the level of a one-semester course in physics. ... these lecture notes are of high interest for physicists. But a mathematician will Read more...

 
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   schema:description "This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators, and the dimensions of the representations of all classical Lie algebras. For this new edition, the text has been carefully revised and expanded; in particular, a new chapter has been added on the deformation and contraction of Lie algebras. ~%#~8232;~%#~8232;~%#~8232; From the reviews of the first edition: ~%#~8232;~%#~8232; "Iachello has written a pedagogical and straightforward presentation of Lie algebras [...]. It is a great text to accompany a course on Lie algebras and their physical applications." (Marc de Montigny, Mathematical Reviews, Issue, 2007 i) ~%#~8232;~%#~8232; "This book [...] written by one of the leading experts in the field [...] will certainly be of great use for students or specialists that want to refresh their knowledge on Lie algebras applied to physics. [...] An excellent reference for those interested in acquiring practical experience [...] and leaving the embarrassing theoretical presentations aside." (Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1156, 2009)."@en ;
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