Re: [問題] 群論
這個用Young tableaux來看還蠻有趣的
_
□ x □ = □□ + □ (3 x 3 = 6 + 3 )
□
□□ x □ = □□□ + □□ (6 x 3 = 10 + 8)
□
_
□ x □ = □□ + □ (3 x 3 = 8 + 1)
□ □ □
□
=> 3 x 3 x 3 = 1 + 8 + 8 + 10
簡單說明一下:
□□□ ijk
□□ = A i,j,k symmetrized & m,n antisymmetrized with i,j
mn
也就是說橫的Symmetrized 直的Antisym
所以SU(3)的話 □ 所有index都antisymmetrize掉了 所以= 1
□
□
細節請參考 Georgi的 Lie Algebras in Particle physics
※ 引述《Farady (月光傳說)》之銘言：
: 借用一下標題，
: 有沒有人知道 3x3x3=1+8+8+10
: 這個式子要怎麼證明?
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◆ From: 71.167.20.130
※ 編輯: breedy 來自: 71.167.20.130 (02/19 00:13)
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