FeynCalc manual (development version)

SUNT

SUNT[a] is the SU(N)SU(N) TaT^a generator in the fundamental representation. The fundamental indices are implicit.

See also

Overview, CA, CF, SUND, SUNDelta, SUNF, SUNSimplify.

Examples

SUNT[a]

TaT^a

Since TaT^a is a noncommutative object, products have to separated by a Dot (.).

SUNT[a] . SUNT[b] . SUNT[c]

Ta.Tb.TcT^a.T^b.T^c

SUNT[a, b, c, d]

Ta.Tb.Tc.TdT^a.T^b.T^c.T^d

SUNSimplify[SUNT[a, b, a], SUNNToCACF -> False]

Tb2N-\frac{T^b}{2 N}

SUNSimplify[SUNT[a, b, b, a]]

CF2C_F^2

SUNSimplify[SUNT[a, b, a]]

12Tb(CA2CF)-\frac{1}{2} T^b \left(C_A-2 C_F\right)

SUNSimplify[SUNT[a, b, a], SUNNToCACF -> False]

Tb2N-\frac{T^b}{2 N}

The normalization of the generators is chosen in the standard way, therefore Tr(TaTb)=12δab\textrm{Tr}(T^aT^b) = \frac{1}{2} \delta _{ab}

SUNTrace[SUNT[a, b]]

δab2\frac{\delta ^{ab}}{2}

In case you want TfT_f, you need to include a factor 2*Tfinside the trace.

SUNTrace[2 Tf SUNT[a, b]]

TfδabT_f \delta ^{ab}

SUNTrace[SUNT[a, b]] // StandardForm

12  SUNDelta[SUNIndex[a],SUNIndex[b]]\frac{1}{2} \;\text{SUNDelta}[\text{SUNIndex}[a],\text{SUNIndex}[b]]

SUNT[a] // FCI // StandardForm

(*SUNT[SUNIndex[a]]*)
SUNT[a] // FCI // FCE // StandardForm

(*SUNT[a]*)