In Eq. (6.2.168) we showed, using its vacuum expectation value form, that (D_{F}(x-y)) satisfied (left(partial_{x}^{2}+m^{2} ight) D_{F}(x-y)=-i

In Eq. (6.2.168) we showed, using its vacuum expectation value form, that \(D_{F}(x-y)\) satisfied \(\left(\partial_{x}^{2}+m^{2}\right) D_{F}(x-y)=-i \delta(x-y)\). Using their vacuum expectation value forms, similarly show that this is true for each of \(D_{\text {ret }}(x-y), D_{\text {adv }}(x-y)\) and \(\bar{D}_{F}(x-y)\).