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)
