Representations of <i>SU</i> (2)

Adam M. Bincer

in Lie Groups and Lie Algebras

Published in print October 2012 | ISBN: 9780199662920
Published online January 2013 | e-ISBN: 9780191745492 | DOI:
Representations of SU (2)

More Like This

Show all results sharing this subject:

  • Mathematical and Statistical Physics


Show Summary Details


Irreducible representations of SU(2) are defined. Eigenstates of J 3 to the eigenvalue m are introduced. Finite-dimensional representations have a so-called highest-weight state for which this eigenvalue is called j and the chapter shows that 2j must be a non-negative integer. It follows that these representations are (2j+1)-dimensional and that the quadratic Casimir operator has the eigenvalue j(j+1). Next addition of angular momentum is discussed, the Clebsch-Gordan series is described, and explicit values for Clebsch–Gordan coefficients are given when one of the angular momenta in the addition is 1/2 or 1. Spherical tensors are defined, the Wigner–Eckart theorem is demonstrated and reduced matrix elements are introduced. Inner and outer multiplicity is defined and SU(2) is shown to be multiplicity-free. Biographical notes on Casimir, Weyl, Clebsch, Gordan and Wigner are given.

Keywords: irreducible representations; highest-weight state; quadratic Casimir; angular momentum addition; Clebsch–Gordan series; Wigner–Eckart theorem; multiplicity

Chapter.  6811 words. 

Subjects: Mathematical and Statistical Physics

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.