  In the framework of a general scalar-tensor theory, we investigate the
equivalence between two different parametrizations of fields that are commonly
used in cosmology - the so-called Jordan frame and Einstein frame. While it is
clear that both parametrizations are mathematically equivalent at the level of
the classical action, the question about their mathematical equivalence at the
quantum level as well as their physical equivalence is still a matter of debate
in cosmology. We analyze whether the mathematical equivalence still holds when
the first quantum corrections are taken into account. We explicitly calculate
the one-loop divergences in both parametrizations by using the generalized
Schwinger-DeWitt algorithm and compare both results. We find that the quantum
corrections do not coincide off shell and hence induce an off shell dependence
on the parametrization. According to the equivalence theorem, the one-loop
divergences should however coincide on shell. For a cosmological background, we
show explicitly that the on shell equivalence is indeed realized by a
nontrivial cancellation.
