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


\!\(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[2]:= SUNSimplify[SUNT[a].SUNT[l].SUNT[c].SUNT[l].SUNT[a].SUNT[c],SUNNToCACF\[Rule] False]

Out[2]= \!\(TraditionalForm\`\((N\^2 - 1)\)\^3\/\(8\ N\^3\)\)

Now changing the name of the dummy varibale l to e in SUNT we get.

In[3]:= SUNSimplify[SUNT[a].SUNT[e].SUNT[c].SUNT[e].SUNT[a].SUNT[c],SUNNToCACF\[Rule] False]

Out[3]= \!\(TraditionalForm\`\(-\(\((N\^2 - 1)\)\^2\/\(8\ N\^3\)\)\)\)) --

Please let me know if I am doing anything wrong, because I really want to do one project using FeynCalc in which performing SU(3) contractions numerically is the essential part.

Best, Hrayr

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