Investigating the Ultraviolet Properties of Gravity with a W(21)
时间:2025-07-10
时间:2025-07-10
We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian r
Thecalculationin[8]proceededasfollows.ThebackgroundmetricischosentobethatofEuclideandeSitterspace.Themodi edinversepropagatorisobtainedfrom(33)justreplacing 2byPk( 2).Usingthepropertiesoftheprojectors,itsinversionistrivial:
Γ(2)+R 121
kk=P2
k 2Λ+d 3d+4d 2P (38)
dR
Decomposinginthesamewaythetermd
tRk+ηRk
dt=1
Pδ tRk
k 2Λ+d2 3d+42TrxLPν.
dR TrxLµ
d
Onecannowexpandto rstorderinR,usethetraces(32)andformula(A10)toobtain:
dΓk
(4π)d/2 dx√
Pk
d(d+ 2Λ dQd+1)tRk+ηRk
2 16Qd
d(d 1)
2 4Qd tRk+ηRk2 Pk Pk tRk
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