38
12. Global Non-Abelian Symmetries
elements are given by (12.48), and verify that they satisfy the SU(2) commutation relations (12.47).
12.6 Verify (12.62).
12.7 Show that a general Hermitian traceless 3 × 3 matrix is parametrized
by 8 real numbers.
12.8 Check that (12.84) is consistent with (12.80) and the infinitesimal form
(8)
of (12.81), and verify that the matrices G a defined by (12.84) satisfy the
commutation relations (12.83).
12.9 Verify, by comparing the coefficients of ∈ 1 , ∈ 2 and ∈ 3 on both sides of
(12.99), that (12.100) follows from (12.99).
12.10 Verify that the operators T ˆ
(
1
2 )
defined by (12.101) satisfy (12.100).
(Note: use the anticommutation relations of the fermionic operators.)
1
2
( )
12.11 Verify that the operators T ˆ
given by (12.101) satisfy the commutation relations (12.103).