χ
αÂα
½
Š g
ð Þ ¼
X
k
X
l
D
αÂα
½
Š g
ð Þ
n
o
kl,kl
¼
1
2
X
k
X
l
D
α
ð Þ
kk g
ð ÞD
α
ð Þ
ll g
ð Þ þ D
α
ð Þ
lk g
ð ÞD
α
ð Þ
kl g
ð Þ
h
i
¼
1
2
χ
α
ð Þ g
ð Þ
h
i 2 þ χ
α
ð Þ g
2
À Á
h
i
&
'
:
ð18:219Þ
Similarly we have
χ
αÂα
f
g g
ð Þ ¼
1
2
χ
α
ð Þ g
ð Þ
h
i 2 À χ
α
ð Þ g
2
À Á
h
i
&
'
:
ð18:220Þ
References
1. Inui T, Tanabe Y, Onodera Y (1990) Group theory and its applications in physics. Springer,
Berlin
2. Inui T, Tanabe Y, Onodera Y (1980) Group theory and its applications in physics, expanded
ed. Shokabo, Tokyo. (in Japanese)
3. Hassani S (2006) Mathematical physics. Springer, New York
4. Chen JQ, Ping J, Wang F (2002) Group representation theory for physicists, 2nd edn. World
Scientific, Singapore
5. Hamermesh M (1989) Group theory and its application to physical problems. Dover, New York
References
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