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Lie algebras and applications / Francesco Iachello.

By: Iachello, Francesco.
Material type: TextTextSeries: Lecture notes in physics ; v 891.Publisher: Berlin : Springer-Verlag, 2015Edition: 2nd ed.Description: xviii, 272 p. : illustrations ; 24 cm.ISBN: 9783662444931 (hard cover : alk. paper).Subject(s): Lie algebrasDDC classification: 512.55
Contents:
1. Basic Concepts -- 2. Semisimple Lie Algebras -- 3. Lie Groups -- 4. Lie Algebras and Lie Groups -- 5. Homogeneous and Symmetric Spaces (Coset Spaces). -- 6. Irreducible Bases (Representations) -- 7. Casimir Operators and Their Eigenvalues -- 8. Tensor Operators -- 9. Boson Realizations -- 10. Fermion Realizations -- 11. Differential Realizations -- 12. Matrix Realizations -- 13. Coset Spaces -- 14. Spectrum Generating Algebras and Dynamic Symmetries -- 15. Degeneracy Algebras and Dynamical Alebras -- References-- Index.
Summary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.55 Ia11 (Browse shelf) Available 136166
Total holds: 0

Includes bibliographical references and index.

1. Basic Concepts --
2. Semisimple Lie Algebras --
3. Lie Groups --
4. Lie Algebras and Lie Groups --
5. Homogeneous and Symmetric Spaces (Coset Spaces). --
6. Irreducible Bases (Representations) --
7. Casimir Operators and Their Eigenvalues --
8. Tensor Operators --
9. Boson Realizations --
10. Fermion Realizations --
11. Differential Realizations --
12. Matrix Realizations --
13. Coset Spaces --
14. Spectrum Generating Algebras and Dynamic Symmetries --
15. Degeneracy Algebras and Dynamical Alebras --
References--
Index.

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.

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