KDE[i, j] is the Kronecker delta in D-4 dimensions.
Overview, CartesianPair, KD, KDD.
KDE[i, j]\hat{\delta }^{ij}
Contract[KDE[i, j] KDE[i, j]]D-4
Contract[KDE[i, j] KD[i, j]]0
Contract[KDE[i, j] KDD[i, j]]D-4
KDE[i, j] // StandardForm
(*KDE[i, j]*)FCI[KDE[i, j]] // StandardForm
(*CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]*)FCE[FCI[KDE[i, j]]] // StandardForm
(*KDE[i, j]*)