Gauge-invariant interaction of spin-3/2 resonances

We show that the gauge-invariant coupling suggested by Pascalutsa removes non-pole terms from the spin-3/2 propagator only for a specific choice of free parameter. For the general case, the problem can be solved by demanding the invariance of the full Lagrangian under the point-like transformations. It is shown that apart from gauge invariance, the original Rarita-Schwinger (R-S) constraint ensures a correct number of physical degrees of freedom. This is used to constrain couplings in the various applications of the half-integer R-S theories in hadron physics.