  We calculate Compton scattering off an elementary spin 3/2 particle in a
recently proposed framework for the description of elementary high spin fields
based on the projection onto eigen-subspaces of the Casimir operators of the
Poincare group. We also calculate this process in the conventional
Rarita-Schwinger formalism. Both formalisms yield the correct Thomson limit but
the predictions for the angular distribution and total cross section differ
beyond this point. We point out that the average squared amplitudes in the
forward direction for Compton scattering off targets with spin s = 0, 1/2, 1
are energy-independent and have the common value 4e^4. As a consequence, in the
rest frame of the particle the differential cross section for Compton
scattering in the forward direction is energy independent and coincides with
the classical squared radius. We show that these properties are also satisfied
by a spin 3/2 target in the Poincare projector formalism but not by the
Rarita-Schwinger spin 3/2 particle.
