Identity tensor has trace 1

Id[a_,b_,p_,q_]:= 1/2 (KroneckerDelta[a,p]KroneckerDelta[b,q]-KroneckerDelta[a,q]KroneckerDelta[b,p])

Sum[ Id[a,b,p,q] Id[p,q,a,b],{a,1,4},{b,1,4},{p,1,4},{q,1,4}]