FeynCalc manual (development version)

SUND

SUND[a, b, c] are the symmetric SU(N)SU(N) dabcd_{abc}.

See also

Overview, SUNDelta, SUNF, SUNSimplify.

Examples

SUND[a, b, c]

dabcd^{abc}

SUND[a, b, c, Explicit -> True]

2(tr(Ta.Tb.Tc))+2(tr(Tb.Ta.Tc))2 \left(\text{tr}(T^a.T^b.T^c)\right)+2 \left(\text{tr}(T^b.T^a.T^c)\right)

SUND[c, a, b]

dabcd^{abc}

SUND[a, b, b]

dabbd^{abb}

SUNSimplify[SUND[a, b, c] SUND[a, b, c]]

2(4CA2)CF-2 \left(4-C_A^2\right) C_F

SUNSimplify[SUND[a, b, c] SUND[a, b, c], SUNNToCACF -> False] // Factor2

(1N2)(4N2)N\frac{\left(1-N^2\right) \left(4-N^2\right)}{N}

SUNSimplify[SUND[a, b, c] SUND[e, b, c], SUNNToCACF -> False] // Factor2

(4N2)δaeN-\frac{\left(4-N^2\right) \delta ^{ae}}{N}

SUND[a, b, c] // StandardForm

(*SUND[a, b, c]*)
SUND[a, b, c] // FCI // StandardForm

(*SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]]*)
SUND[a, b, c] // FCI // FCE // StandardForm

(*SUND[a, b, c]*)