SUNFDelta[a, b]
is the Kronecker-delta for with color indices a
and b
in the fundamental representation.
[SUNFIndex[a], SUNFIndex[b]] SUNFDelta
[SUNFIndex[a], SUNFIndex[b]] SUNFDelta[SUNFIndex[b], SUNFIndex[c]]
SUNFDelta
% // SUNSimplify
[SUNFIndex[a], SUNFIndex[b]]^2
SUNFDelta
% // SUNSimplify
[SUNFIndex[a], SUNFIndex[b]] // StandardForm
SUNFDelta
(*SUNFDelta[SUNFIndex[a], SUNFIndex[b]]*)
[SUNFIndex[a], SUNFIndex[b]] // FCI // FCE // StandardForm
SUNFDelta
(*SDF[a, b]*)
[a, b] // FCI // StandardForm
SDF
(*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.
= SUNFDelta[SUNFIndex[a], ExplicitSUNFIndex[2]] SUNFDelta[SUNFIndex[a], SUNFIndex[b]] SUNFDelta[SUNFIndex[c], ExplicitSUNFIndex[2]] // SUNSimplify ex
// StandardForm
ex
(*SUNFDelta[ExplicitSUNFIndex[2], SUNFIndex[b]] SUNFDelta[ExplicitSUNFIndex[2], SUNFIndex[c]]*)
[1, 2] // FCI // StandardForm
SDF
(*SUNFDelta[ExplicitSUNFIndex[1], ExplicitSUNFIndex[2]]*)