Francesco Iachello

Lie Algebras and Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

From the reviews of the first edition:

"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)

"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)

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 272
• Erscheinungstermin: 13. Oktober 2014
• Englisch
• ISBN-13: 9783662444948
• Artikelnr.: 43791519

Autorenporträt

Iachello is a renowned physicist. Honors: Chiaudano Prize, 1964 Fulbright Fellow, 1968 AKZO Prize of the Netherlands Society of Sciences, 1981 Wigner Medal, 1990 Taormina Prize, 1991 Dr. Hon., University of Ferrara, Italy, 1992 Bonner Prize of the American Physical Society, 1993 Dr. Hon., University of Seville, Spain, 1993 Ph.D. Hon. Chung Yuan University, Republic of China, 1993 Honorary Professor Nanjing University, China, 1995 Foreign Member Royal Netherlands Academy of Arts and Sciences, 1996 Honorary Fellow Eotvos Physical Society, Hungary, 1996 Centennial Prize of the Italian Physical Society, 1997 Foreign Member Croatian Academy of Arts and Sciences, 1997 Zernike Professor University of Groningen, The Netherlands, 1997 Eminent Scientist Award, RIKEN, Tokyo, Japan, 2000 Meitner Prize of the European Physical Society 2002 Dr. Hon., University of Bucharest, Romania, 2005 Italian National Medal of Science, 2007 Majorana Prize, 2007 Commemorative Medal, University of Prague, Czech Republic, 2008

Inhaltsangabe

Basic Concepts.- Semisimple Lie Algebras.- Lie Groups.- Irreducible Bases (Representations).- Casimir Operators and Their Eigenvalues.- Tensor Operators.- Boson Realizations.- Fermion Realizations.- Differential Realizations.- Matrix Realizations.- Spectrum Generating Algebras and Dynamic Symmetries.- Degeneracy Algebras and Dynamical Algebras.

Rezensionen

From the reviews: "Iachello has written a pedagogical and straightforward presentation of Lie algebras and some applications to bosonic systems encountered in molecular, atomic, nuclear and particle physics. ... The book should be of interest to graduate students and researchers in physics, although mathematicians and chemists should find it useful as well. It is a great text to accompany a course on Lie algebras and their physical applications." (Marc de Montigny, Mathematical Reviews, Issue, 2007 i) "This book ... a practical introduction to important facts concerning Lie algebras that continuously appear in physical problems, and written by one of the leading experts in the field. ... the book 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 in the application and techniques of Lie algebras to physics, and leaving the embarrassing theoretical presentations aside." (Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1156, 2009)