Second order formalism for spin 1/2 fermions and Compton scattering

We develop a second order formalism for massive spin 1/2 fermions based on the projection over Poincare invariant subspaces in the (1/2, 0) circle plus (0, 1/2) representation of the homogeneous Lorentz group. Using the U(1)(em) gauge principle we obtain a second order description for the electromagnetic interactions of a spin 1/2 fermion with two free parameters, the gyromagnetic factor g and a parameter xi related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case g 2, xi = 0, and for states with well-defined parity, we recover Dirac results. In general, we find the correct classical limit and a finite value r(c)(2) for the forward differential cross section, independent of the photon energy and of the value of the parameters g and xi. The differential cross section vanishes at high energies for all g, xi except in the forward direction. The total cross section at high energies vanishes only for g = 2, xi = 0. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.