Lie Algebras and Applications

  • Francesco¬†Iachello

Part of the Lecture Notes in Physics book series (LNP, volume 708)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Francesco Iachello
    Pages 1-13
  3. Francesco Iachello
    Pages 15-25
  4. Francesco Iachello
    Pages 27-38
  5. Francesco Iachello
    Pages 39-62
  6. Francesco Iachello
    Pages 63-74
  7. Francesco Iachello
    Pages 75-89
  8. Francesco Iachello
    Pages 91-130
  9. Francesco Iachello
    Pages 131-146
  10. Francesco Iachello
    Pages 147-153
  11. Francesco Iachello
    Pages 155-162
  12. Francesco Iachello
    Pages 163-172
  13. Francesco Iachello
    Pages 173-188
  14. Back Matter
    Pages 179-190

About this book


This book, designed for advanced graduate students and post-graduate researchers, provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, a concise exposition is given of the basic concepts of Lie algebras, their representations and their invariants. The second part contains 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 contains many examples that help to elucidate the abstract algebraic definitions. It provides 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.


Abstract algebra Boson Eigenvalue Matrix Quark hadron molecule

Authors and affiliations

  • Francesco¬†Iachello
    • 1
  1. 1.Department of PhysicsYale UniversityNew HavenUSA

Bibliographic information

Industry Sectors
Energy, Utilities & Environment