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020 _a9783662444948
_9978-3-662-44494-8
024 7 _a10.1007/978-3-662-44494-8
_2doi
050 4 _aQC5.53
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.15
_223
100 1 _aIachello, Francesco.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLie Algebras and Applications
_h[electronic resource] /
_cby Francesco Iachello.
250 _a2nd ed. 2015.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2015.
300 _aXVIII, 272 p. 37 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v891
505 0 _aBasic Concepts -- Semisimple Lie Algebras -- Lie Groups -- Lie Algebras and Lie Groups -- Homogeneous and Symmetric Spaces (Coset Spaces). - Irreducible Bases (Representations) -- Casimir Operators and Their Eigenvalues -- Tensor Operators -- Boson Realizations -- Fermion Realizations -- Differential Realizations -- Matrix Realizations -- Coset Spaces -- Spectrum Generating Algebras and Dynamic Symmetries -- Degeneracy Algebras and Dynamical Alebras -- Index.
520 _aThis 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).
650 0 _aMathematical physics.
650 0 _aQuantum theory.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aParticle and Nuclear Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P23002
650 2 4 _aAtomic, Molecular, Optical and Plasma Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P24009
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662444931
776 0 8 _iPrinted edition:
_z9783662444955
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v891
856 4 0 _uhttps://doi.org/10.1007/978-3-662-44494-8
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c10298
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