Structure constants of SU(N)

1. Oct 5, 2008

Lester

Hi there,

Does anybody know how to exploit the product of structure constants of SU(N) through Kroenecker deltas? I mean

$$\sum_a f_{abc}f_{ade}$$

I know this for SU(2) as in this case I have the Levi-Civita symbol but in other cases I was not able to recover it in literature. Any help appreciated.

Jon

2. Oct 7, 2008

3. Oct 8, 2008

Lester

Thanks a lot Sam. This was the formula I was looking for.

Jon

4. Jun 22, 2011

MudassarSabir

Dear Sam & Lester

Can you please tell me any book reference for these identities involving $d^{abc}$ in jacobi identity and the structure constants contraction.

5. Jun 22, 2011

MudassarSabir

Dear samalkhaiat

Your formula for jacobi identity is wrong. Actually it should have all d^{abc} instead of the f^{abc} everywhere. The correct Jacobi identity is:

$$d^{ace}d^{bde}+d^{ade}d^{bce}+d^{bae}d^{cde}=0$$

Kindly provide me any references for contraction formula for structure constants of SU(N).

Thanks.