  We show how to map gravitational theories formulated in the Jordan frame to
the Einstein frame at the quantum field theoretical level considering quantum
fields in curved space-time. As an example, we consider gravitational theories
in the Jordan frame of the type $F(\phi,\, R)=f(\phi)\, R-V(\phi)$ and perform
the map to the Einstein frame. Our results can easily be extended to any
gravitational theory. We consider the Higgs inflation model as an application
of our results.
