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I'm trying to study renormalization in QFT in curved spacetime. So let's say we have a fixed de Sitter background and we have an interacting theory (e.g. massive $\lambda \phi^4$) and I'm going to calculate the one-loop correction to the $\phi$ propagator in the in-in framework.

If I regularize the amputated amplitude with a hard cut-off $\Lambda$, using WKB approximated propagator, I should find something like

$$ A_{\rm amp}\sim \Lambda^2 - m^2 \ln (\Lambda/m) $$

from here I could define a counter-term that is time-independent and have the amplitude regularized. Is it enough? Am I missing something?

  1. Is it the correct way to proceed and renormalize a QFT in Curved Spacetimes? Can I define counterterms from an amplitude where I used approximated propagators?

  2. Is this procedure called adiabatic renormalization?

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Have you looked at Ian Drummond's DIMENSIONAL REGULARIZATION OF MASSLESS THEORIES IN SPHERICAL SPACE-TIME Nucl. Phys. B 94 (1975) pp115-144?

Lot's of useful info about how to do renormalization in (Euclidean) de Sitter space. Ian has several other papers on this subject at about the same date.

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  • $\begingroup$ Thanks, I will also look at the other papers but I was more interested in a cut off regularization methos $\endgroup$
    – TheoPhy
    Commented Jun 6, 2020 at 19:03

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