# How do I find the values for the structure constants ($f^{abc}$) of a gauge group?

How do I find the values for the structure constants ($$f^{abc}$$) of a gauge group, as a mean to find the tree-level amplitude for a process in which one of the tree-level diagrams is:

the process being: $$Z_L(p_1) +Z_L(p_2) \to Z_L(p_3) + Z_L(p_4)$$

## 1 Answer

They depend on the group and the basis you choose for the generators. There is no simple recipe, but for calculating physical quantities you should never need to know the individual $$f_{abc}$$'s. All physical quantities can be computed from the various Casimirs. A good source for how this works for field theory is the book "Group Theory: Birdtracks, Lie's, and Exceptional Groups" by Predrag Cvitanović

• Thank you for your help. – user7077252 Mar 15 at 17:10