We will show that there is no divergence inK µαβ(ω1, ω2) in the static limitω 1, ω2 →0

No divergence in the static limit The response functionK µαβ(ω1, ω2) at the Matsubara frequency is given as, K µαβ(iω1,iω 2) =− 1 2 e ℏ 3 iω′,a α,iω 1 β,iω 2 µ,iω 1 +iω 2 − 1 2 e