Transversality of the Rarita-Schwinger self-energy, Ward identities, and dimensional regularization

The finite one-loop parts of the Rarita-Schwinger self-energy in the gauge $\alpha \gamma ·\psi +(1-\alpha ){\gamma }^a{\delta }_a^{\mu }{\psi }_{\mu }$ satisfy the transversality Ward identity in the new regularization scheme by dimensional reduction but not in conventional dimensional regularization. Diagonalizing and then omitting the nonpropagating Lorentz ghosts, new vertices in the non-Lorentz ghost sectors do contribute. The criteria for deriving Ward identities involving tracelessness of structure constants are shown to be equivalent to the unit Becchi-Rouet-Stora-Tyutin Jacobian provided the gauge algebra closes.