Frame Transformations of Gravitational Theories

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 $F(ϕ,\, R)=f(ϕ)\, R-V(ϕ)$ 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.

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