Poincaré invariance of the spin-3/2 field in the presence of a minimal external electromagnetic interaction

Using the action principle, we determine the Poincaré transformation properties of second-quantized fields in the presence of external fields. We then construct expressions for the generators of the Poincaré group and explicitly verify that a second-quantized spin-3/2 field interacting with a minimal external electromagnetic field transforms covariantly. We thus conclude that the negative metric which appears in the quantization of the spin-3/2 field is not the result of a noncovariant quantization as has been claimed