FeynCalc manual (development version)

SUNF

SUNF[a, b, c] are the structure constants of SU(N). The arguments a, b, c should be of symbolic type.

See also

Overview, SUND, SUNDelta, SUNIndex, SUNSimplify, SUNT, Trick.

Examples

SUNF[a, b, c] x + SUNF[b, a, c] 
 
Calc[%] 
 
SUNSimplify[%%]

x f^{abc}+f^{bac}

x f^{abc}-f^{abc}

(x-1) f^{abc}

SUNF[a, a, b] 
 
% // Calc

f^{aab}

0

This is a consequence of the usual choice for the normalization of the T_a generators.

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

2 i \left(\text{tr}(T^a.T^c.T^b)-\text{tr}(T^a.T^b.T^c)\right)

SUNSimplify[SUNF[a, b, c] SUNF[a, b, d]]

C_A \delta ^{cd}

SUNSimplify[SUNF[a, b, c], Explicit -> True]

-2 i \left(\text{tr}(T^a.T^b.T^c)-\text{tr}(T^b.T^a.T^c)\right)

SUNF[a, b, c] // StandardForm

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

SUNF[a, b, c] // FCI // StandardForm

(*SUNF[SUNIndex[a], SUNIndex[b], SUNIndex[c]]*)

SUNF[a, b, c] // FCI // FCE // StandardForm

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

SUNF[b, a, c] 
 
% // FCI

f^{bac}

-f^{abc}