Lie Algebras and Applications

Francesco Iachello

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
27 October 2014

Mathematics & Sciences; Physics; Atomic & molecular physics; Quantum physics (quantum mechanics & quantum field theory); Mathematical physics

Series: Lecture Notes in Physics

"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)"

By: Francesco Iachello
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2nd ed. 2015
Volume: 891
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 4.453kg
ISBN: 9783662444931
ISBN 10: 3662444933
Series: Lecture Notes in Physics
Pages: 272
Publication Date: 27 October 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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

Reviews for Lie Algebras and Applications

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 also find it interesting to see Lie algebras `in action' in physics. There are a lot of detailed examples available in the book. (Martin Schlichenmaier, Mathematical Reviews, January, 2016)