This course-based primer offers an creation to Lie algebras and a few in their purposes to the spectroscopy of molecules, atoms, nuclei and hadrons. within the first half, it concisely offers the fundamental recommendations of Lie algebras, their representations and their invariants. the second one half features a description of the way Lie algebras are utilized in perform within the therapy of bosonic and fermionic structures. actual purposes thought of contain rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell version, the nuclear shell version, and the quark version of hadrons. one of many key options within the program of Lie algebraic tools in physics, that of spectrum producing algebras and their linked dynamic symmetries, is usually mentioned. The booklet highlights a couple of examples that support to demonstrate the summary algebraic definitions and contains a precis of many formulation of sensible curiosity, resembling the eigenvalues of Casimir operators, and the size of the representations of all classical Lie algebras.
For this new version, the textual content has been rigorously revised and extended; particularly, a brand new bankruptcy has been extra at the deformation and contraction of Lie algebras.
From the experiences of the 1st edition:
"Iachello has written a pedagogical and simple presentation of Lie algebras [...]. it's a nice textual content to accompany a path on Lie algebras and their actual applications."
(Marc de Montigny, Mathematical stories, factor, 2007 i)
"This ebook [...] written through one of many major specialists within the box [...] will surely be of serious use for college kids or experts that are looking to refresh their wisdom on Lie algebras utilized to physics. [...] a great reference for these drawn to buying sensible event [...] and leaving the embarrassing theoretical displays aside."
(Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1156, 2009)