Fermionic α-vacua

A spin (1/2) particle propagating in a de Sitter background has a one parameter family of states which transform covariantly under the isometry group of the background. These states are the fermionic analogues of the α-vacua for a scalar field. We shall show how using a point-source propagator for a fermion in an α-state produces divergent perturbative corrections. These corrections cannot be used to cancel similar divergences arising from scalar fields in bosonic α-vacua since they have an incompatible dependence on the external momenta. The theory can be regularized by modifying the propagator to include an antipodal source