Effective action and decoherence by fermions in quantum cosmology

We develop the formalism for the one-loop no-boundary state in a cosmologic al model with fermions. We use it to calculate the reduced density matrix f or an inflaton field by tracing out the fermionic degrees of freedom, yield ing both the fermionic effective action and the standard decoherence factor . We show that dimensional regularisation of ultraviolet divergences would lead to an inconsistent density matrix. Suppression of these divergences to zero is instead performed through a non-local Bogoliubov transformation of the fermionic variables, which leads to a consistent density matrix. The r esulting degree of decoherence is less than in the case of bosonic fields. (C) 1999 Elsevier Science B.V. All rights reserved.