Electromagnetic interaction of higher-spin fields

The electromagnetic interaction of fields of spins $\frac{3}{2}$ and 2 is investigated with the use of the ghost-field formalism. It is thus shown that the canonical formalism for interacting higher-spin fields can be developed in a straightforward manner, which avoids the complexities and controversies of the conventional formalism. Our detailed treatment of the Lorentz invariance of the scattering operator and the gauge invariance of the photon self-energy resulting from spin-$\frac{3}{2}$ fermion and spin-2 boson loops shows that the quantum theory of interacting spin-$\frac{3}{2}$ and spin-2 fields does not present any unusual difficulty. However, the electromagnetic interaction of both of these fields is nonrenormalizable, which is expected from power-counting arguments as well as supported by explicit calculations.