Name: Hrayr Matevosyan 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\/\(8\ N\^3\)\)\)\))
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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