FeynCalc manual (development version)

SUNFDelta

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

See also

Overview, SUNDelta.

Examples

SUNFDelta[SUNFIndex[a], SUNFIndex[b]]

\delta _{ab}

SUNFDelta[SUNFIndex[a], SUNFIndex[b]] SUNFDelta[SUNFIndex[b], SUNFIndex[c]] 
 
% // SUNSimplify

\delta _{ab} \delta _{bc}

\delta _{ac}

SUNFDelta[SUNFIndex[a], SUNFIndex[b]]^2 
 
% // SUNSimplify

\delta _{ab}^2

C_A

SUNFDelta[SUNFIndex[a], SUNFIndex[b]] // StandardForm

(*SUNFDelta[SUNFIndex[a], SUNFIndex[b]]*)
SUNFDelta[SUNFIndex[a], SUNFIndex[b]] // FCI // FCE // StandardForm

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

(*SUNFDelta[SUNFIndex[a], SUNFIndex[b]]*)

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

ex = SUNFDelta[SUNFIndex[a], ExplicitSUNFIndex[2]] SUNFDelta[SUNFIndex[a], SUNFIndex[b]] SUNFDelta[SUNFIndex[c], ExplicitSUNFIndex[2]] // SUNSimplify

\delta _{2b} \delta _{2c}

ex // StandardForm

(*SUNFDelta[ExplicitSUNFIndex[2], SUNFIndex[b]] SUNFDelta[ExplicitSUNFIndex[2], SUNFIndex[c]]*)
SDF[1, 2] // FCI // StandardForm

(*SUNFDelta[ExplicitSUNFIndex[1], ExplicitSUNFIndex[2]]*)