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Group Theory


  • General properties of groups (subgroup, coset, quotient group, homomorphism, direct product)
  • Group representations (Irreducible representation, properties, CG coefficient)
  • Finite groups (permutation groups, cyclic groups, classification)
  • Lie groups (SO(3), SU(2), Lie algebra, general properties of simple Lie groups)
  • Application: atomic spectra
  • Application: condensed matter
  • Application: special relativity
  • Application: standard model

Recommended Text Book

  • A. Zee, Group Theory in a Nutshell for Physicists, Princeton University Press, 2016.
  • P. Ramond, Group Theory: A Physicist's Survey, Cambridge Univ. Press, 2010.
  • H. F. Jones, Groups, Representations, and Physics, Institute of Physics Publishing, 2nd ed.,
  • J. F. Cornwell, Group Theory in Physics: An Introduction, Academic Press, 1997.
  • Wu-Ki Tung, Group Theory in Physics, World Scientific, 1985.
  • H. Georgi, Lie Algebras in Particle Physics, Benjamin, 1982.
  • E. P. Wigner, Group Theory, Academic Press, 1959.
  • J. Talman, Special Functions, a Group-Theoretic Approach, Benjamin, 1968.
  • M. Tinkham, Group Theory and Quantum Mechanics, 1964.