Pure Spin-5/2 Propagator from the Antisymmetric Tensor Spinor Formalism

We have derived the formulation of pure spin-5/2 propagator by using the antisymmetric tensor spinor (ATS) formalism proposed by Acosta et. al. The ATS prescription provides an alternative mechanism to avoid the background problems that appear in the Rarita-Schwinger formulation, e.g., the emergence of lower spin background and the violation of relativity in the electromagnetic field. The carrier space of the spin of interest (5/2, 0) circle plus (0, 5/2) of SO(1,3) is embedded into a reducible space constructed by the tensor product of antisymmetric tensor; the antisymmetric tensor and the Dirac spinor. The pure spin-5/2 sector is extracted by the projection operator in the basis constructed by the Casimir operator in terms of Lorentz-group generator. The propagator is obtained by calculating the inverse of the equation of motion. We used Feyncalc to simplify the calculation.