Investigating the Ultraviolet Properties of Gravity with a W(10)
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
TheERGEcanbeseenformallyasaRG–improvedoneloopequation.Toseethis,recallthatgivenabareactionS(forabosonic eld),theoneloope ectiveactionΓ(1)is
1Γ(1)=S+.δφδφ
LetusaddtoSthecuto term(7);thefunctional
Γk=S+(1)(12)1
δφδφ+Rk, (13)
maybecalledthe“oneloopaveragee ectiveaction”.Itsatis estheequation
k(1)dΓk
2Tr δ2S
dk,(14)
whichisformallyidenticalto(9)exceptthatinther.h.s.therenormalizedrunningcou-plingsgi(k)arereplacedeverywherebythe“bare”couplingsgi,appearinginS.Thusthe“RGimprovement”intheERGEconsistsinreplacingthebarecouplingsbytherunningrenormalizedcouplings.Inthisconnection,notethatingeneralthecuto functionRkmaycontainthecouplingsgiandthereforethetermkd
dkRkinther.h.s.goestozeroformomentagreaterthankand
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