Fierz identity using SUNSimplify

[AlessioV01]

I want to use SUNSimplify to compute the Fierz identity for SU(N):
$\sum_{a}T^a_{ij}T^a_{kl} = \frac{1}{2}\left(\delta_{il}\delta_{kj} - \frac{1}{N}\delta_{ij}\delta_{kl} \right)$.

I tried using it:
SUNSimplify[SUNTF[{a}, i, j] SUNTF[{a}, k, l]]
but the result that I have is T^{FCGV(sun2611)}{ij}T^{FCGV(sun2611)}{kl}

Why it does not actually simplify this expression? How can I fix this problem?

[vsht]

Unfortunately, SUNSimplify doesn't support Fierz identities. You can still implement it by hand using suitable replacement rules. Am 11.01.25 um 15:11 schrieb AlessioV01:

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I want to use *SUNSimplify* to compute the Fierz identity for SU(N): $\sum_{a}T^a_{ij}T^a_{kl} = \frac{1}{2}\left(\delta_{il}\delta_{kj} - \frac{1}{N}\delta_{ij}\delta_{kl} \right)$. I tried using it: SUNSimplify[SUNTF[{a}, i, j] SUNTF[{a}, k, l]] but the result that I have is T^{FCGV(sun2611)}/{ij}T^{FCGV(sun2611)}/{kl} Why it does not actually simplify this expression? How can I fix this problem? — Reply to this email directly, view it on GitHub <https://github.com/ FeynCalc/feyncalc#296>, or unsubscribe <https://github.com/ notifications/unsubscribe-auth/ ABXSD5GJT5ILPQQPPCDSSXL2KERADAVCNFSM6AAAAABVAAIHN2VHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZXHAYDQNRQGI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>