Propagation of a massive spin-3/2 particle

Abstract

The propagation of an off-shell spin-3/2 baryon is investigated in a consistent framework using projections corresponding to one irreducible spin-3/2 and two irreducible spin-1/2 representations arising from the usual spinor-vector representation of the spin-3/2 fields. Starting from the most general Lagrangian invariant under point transformations containing first-order derivatives only and imposing the constraint $\gamma_\mu \psi^\mu=0$, we eliminate one of the spin-1/2 contributions. The resulting propagator provides a clean separation of spin-3/2 proper and the one remaining spin-1/2 contribution. In addition to a conventional pole term describing pure spin-3/2, which is identical to the propagator proposed by Williams, this procedure yields a second pole term describing spin-1/2 only, with a pole at twice the mass parameter of the Lagrangian. Its effect on physical observables may manifest itself in a manner which is indistinguishable from a particle in its own right. The second pole term cancels the $1/p^2$ singularity of the Williams propagator and the propagator derived here is well behaved for vanishing $p^2$.