Investigating the Ultraviolet Properties of Gravity with a W(19)
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
ofthetype:
SGF(g(B),h)=
whereZg(B)χµg(B)µνχν,1+ρ(29)χν= µhµν
2
includingthegauge xingterm,canbewrittenintheform
1
containingtheminimaloperator:
Γk
where8(2)µνρσ 1,whichleadstoconsiderablesimpli cation.Theinversepropagatorofhµν,ghµνΓk(2)µνρσhρσ µν µν=ZKρσ( 2 2Λ)+Uρσ,
;µνδρσ=(30)µνKρσ=1
2
1µνPρσ 1dgµνgρσ;µνµνUρσ=RKρσ+
gh.dµνUsingthatK=1
2
equation(30)ineitherofthefollowingforms:
Γk(2) P,ifd=2wecanrewrite=ZK( 2 2Λ1+W)Z=2 P 2 2Λ1 4
2(d 2)(Rρσgµν+gρσRµν Rgρσgµν).
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