  Electromagnetic interactions of the spin 3/2 particle are investigated while
allowing the propagation of the transverse spin 1/2 component present in the
reducible Rarita-Schwinger vector-spinor. This is done by allowing a more
general form for the mass term, while leaving the kinetic terms untouched. We
find that the interaction is consistent and does not lead to superluminal
propagation for a range of the mass of the spin 1/2 particle, except for the
special point where the spin 1/2 particle is infinitely massive. We then
quantize the theory using the appropriate Grassmann-variable path integral and
study the poles of the propagator. The unfamiliar feature of the theory is that
the charge matrix is not positive definite; it is positive definite on the
space of spin 3/2 solutions, and negative definite on the space of spin 1/2
solutions. Classically, for spin 1/2 modes the energy is of the opposite sign
to frequency, i.e. the positive frequency modes have negative energy. It is
found that the retarded part appropriately propagates the positive energy
solutions forward in time, while the advanced part propagates the negative
energy solutions back in time so long as the free parameter is chosen such that
the positive frequency modes have the same parity. The propagator contains
poles of the spin 1/2 modes above the real axis for the positive and below the
real axis for the negative frequency modes, while the residues at those poles
are also of the sign opposite to the usual; altogether this leads to a unitary
S-matrix, the forward amplitude <p|p> being positive for all modes. The
canonically quantized field is causal, and the equal-time anti-commutator has
positive definite form. We choose the physical vacuum as the highest-weight
state with respect to the spin 1/2 operators in order to have positive energy,
and to correctly reproduce both the unusual residues and locations of the
poles.
