By Francesco Iachello

This course-based primer presents 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 provides the elemental innovations of Lie algebras, their representations and their invariants. the second one half contains a description of ways Lie algebras are utilized in perform within the therapy of bosonic and fermionic platforms. actual functions 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 suggestions within the software of Lie algebraic equipment in physics, that of spectrum producing algebras and their linked dynamic symmetries, can be mentioned. The publication highlights a few examples that support to demonstrate the summary algebraic definitions and incorporates a precis of many formulation of sensible curiosity, corresponding to the eigenvalues of Casimir operators, and the size of the representations of all classical Lie algebras.

For this re-creation, the textual content has been conscientiously revised and accelerated; specifically, a brand new bankruptcy has been additional at the deformation and contraction of Lie algebras.

From the studies of the 1st edition:

"Iachello has written a pedagogical and easy presentation of Lie algebras [...]. it's a nice textual content to accompany a direction on Lie algebras and their actual applications."

(Marc de Montigny, Mathematical reports, factor, 2007 i)

"This ebook [...] written via one of many prime 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 attracted to buying useful adventure [...] and leaving the embarrassing theoretical shows aside."

(Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1156, 2009)

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