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[4]:=
SUNSimplify[SUNT[a].SUNT[l].SUNT[c].SUNT[l].SUNT[a].SUNT[c],SUNNToCACF\[Rule]
      True]

Out[4]=
\!\(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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