Not sure if this is the correct forum but here goes.(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to prove [T^{a},T^{b}] = if^{abc}T^{c}

Where (T^{a})^{bc}= -if^{abc}and f^{abc}are the structure constants for SU(3).

I picked f^{123 }and generated the three 8 x 8 matrices .. T^{1}, T^{2}and T^{3}.

The matrices components are all 0 except for,

(T^{1})^{23}= -i

(T(^{1})^{47}= -i/2

(T^{1})^{56}= i/2

(T^{2})^{46}= -i/2

(T^{2})^{57}= -i/2

(T^{3})^{45}= -i/2

(T^{3})^{67}= i/2

When I compute [T^{1},T^{2}] I get 0. What am I missing?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Adjoint representation of SU(3)

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**