Electromagnetic currents of elementary particles from a second order formalism

We use a second order formalism based on Poincaré symmetry, and known as Covariant Projector Formalism to calculate the electromagnetic currents of spin 1/2, spin 1 and spin 3/2 particles. We restrict to parity conserving processes and obtain the currents in terms of the gyromagnetic factor g alone. This parameter is then fixed by calculating the forward Compton scattering cross section. In the end we reproduce the Dirac moments for the electron from a more general second order Lagrangian, we also reproduce the Standard Model results for the W boson. In the spin 3/2 case we show that the RS current is incomplete as it does not include the spin 1 piece of the vector-spinor representation. As a consequence, when we calculate the spin 3/2 EM moments, instead of the universal value g = 2, we find g = 2/3 as the gyromagnetic ratio for a Rarita-Schwinger particle.