FeynCalc manual (development version)

SUNDelta

SUNDelta[a, b] is the Kronecker-delta for SU(N) with color indices a and b in the adjoint representation.

See also

Overview, ExplicitSUNIndex, SD, SUNF, SUNIndex, SUNSimplify, Trick.

Examples

SUNDelta[SUNIndex[a], SUNIndex[b]]

\delta ^{ab}

SUNDelta[SUNIndex[a], SUNIndex[b]] SUNDelta[SUNIndex[b], SUNIndex[c]] 
 
SUNSimplify[%]

\delta ^{ab} \delta ^{bc}

\delta ^{ac}

SUNDelta[SUNIndex[a], SUNIndex[b]] // StandardForm

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

(*SD[a, b]*)
SD[a, b] // FCI // StandardForm

(*SUNDelta[SUNIndex[a], SUNIndex[b]]*)

The arguments of SUNDelta may also represent explicit integer indices via the head ExplictiSUNIndex. The difference is that SUNSimplify will only sum over symbolic indices.

ex = SUNDelta[SUNIndex[a], ExplicitSUNIndex[2]] SUNDelta[SUNIndex[a], SUNIndex[b]] SUNDelta[SUNIndex[c], ExplicitSUNIndex[2]] // SUNSimplify

\delta ^{2b} \delta ^{2c}

ex // StandardForm

(*SUNDelta[ExplicitSUNIndex[2], SUNIndex[b]] SUNDelta[ExplicitSUNIndex[2], SUNIndex[c]]*)
SD[1, 2] // FCI // StandardForm

(*SUNDelta[ExplicitSUNIndex[1], ExplicitSUNIndex[2]]*)