Lie Algebras and Applications

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)

“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)

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