Fermionic alpha-vacua
Hael Collins (Carnegie Mellon University, University of, Massachusetts, Amherst)
TL;DR
This paper introduces fermionic alpha-vacua in de Sitter space, analyzes their properties, and discusses how to regularize divergences in fermionic propagators using antipodal sources.
Contribution
It extends the concept of alpha-vacua to fermions, showing their properties and proposing a regularization method involving antipodal sources.
Findings
Fermionic alpha-vacua form a one-parameter family of states.
Point-source propagators in alpha-states lead to divergences.
Regularization with antipodal sources resolves divergences.
Abstract
A spin one-half 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 alpha-vacua for a scalar field. We shall show how using a point-source propagator for a fermion in an alpha-state produces divergent perturbative corrections. These corrections cannot be used to cancel similar divergences arising from scalar fields in bosonic alpha-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.
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