Decoherence and ultraviolet divergences in quantum cosmology

We consider the problem of ultraviolet divergences in the decoherence facto r in quantum cosmology. It is shown that using dimensional regularization i t is not possible to obtained the consistent reduced density matrix. In the case of tracing out the bosonic inhomogeneous degrees of freedom one can g et a reasonable reduced density matrix showing decoherence properties using a conformal reparametrization of fields, which suppresses ultraviolet dive rgences. In the case of fermionic fields such a suppression can be achieved by performing of a non-local Bogoliubov transformation of Grassmann variab les.