Name: Hrayr Matevosyan (email_not_shown)
Date: 02/15/06-12:27:47 AM Z

SUNSimplify doesn't give correct results when contracting 3 pairs of SU(N) generators.

For example

In:=
SUNSimplify[SUNT[a].SUNT[l].SUNT[c].SUNT[l].SUNT[a].SUNT[c],SUNNToCACF\[Rule]
True]

Out=
\!\(TraditionalForm\`\(-\(1\/2\)\)\ \((C\_A - 2\ C\_F)\)\ C\_F\%2\)

IT IS A WRONG RESULT! The result of that contraction is easy to evaluate, and should be
(-(1/2)(C_A - 2*C_F))^2* C_F, and not what SUNSimplify gives: (-(1/2)(C_A - 2*C_F))* C_F^2 .

Similarly wrong results are obtained if one uses different permutations of the SUNTs. SUNSimplify works correctly for two pairs of SUNTs.

```---
Even more weired is that SUNSimplify gives different answers  for the same contractions if one renames the dummy contraction indecies and sets SUNNToCACF \[Rule] False.
For Example:
In:=
SUNSimplify[SUNT[a].SUNT[l].SUNT[c].SUNT[l].SUNT[a].SUNT[c],SUNNToCACF\[Rule]
False]
Out=
Now changing the name of the dummy varibale l to e in SUNT we get.
In:=
SUNSimplify[SUNT[a].SUNT[e].SUNT[c].SUNT[e].SUNT[a].SUNT[c],SUNNToCACF\[Rule]
False]
Out=