On gauge independence in quantum gravity

Vassilevich, D. V.

doi:10.1016/0550-3213(95)00477-a

Cited by 7 publications

(7 citation statements)

References 40 publications

(61 reference statements)

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“…This can be done by fixing the gauge and is most easily achieved by adopting the Feynman-'t Hooft gauge (3.2) where α = 1. However it is possible to factor out the gauge orbit without fixing the gauge [98,[118][119][120] but instead using the freedom to pick coordinates φ a which split the field into physical and gauge degrees of freedom. Gauge independence is then just reflected in the fact that appropriate coordinate systems, corresponding to different gauges, are just related by transformations with a trivial Jacobian.…”

Section: A Perturbative Expansion and Regularisationmentioning

confidence: 99%

Physical renormalization schemes and asymptotic safety in quantum gravity

Falls

2017

Phys. Rev. D

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The methods of the renormalization group and the ε-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ε-expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultra-violet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalisable.

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Section: A Perturbative Expansion and Regularisationmentioning

confidence: 99%

Physical renormalization schemes and asymptotic safety in quantum gravity

Falls

2017

Phys. Rev. D

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“…In particular cases this problem was solved in Refs. [1,[3][4][5]. In a sense, we suggest an extension of the Theorem 1.2 of Ref.…”

Section: Introductionmentioning

confidence: 84%

“…For some values of the constants this operator reduces to that considered previously in the paper [1], where one can find some motivations for studying non-minimal operators. Such operators appear naturally in quantum gauge theories after imposing gauge conditions [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Heat kernel for nonminimal operators on a Kähler manifold

Alexandrov

Vassilevich

1996

Journal of Mathematical Physics

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“…[23], in which the author calculated the one-loop effective action for Einstein gravity within a special class of background gauges and found the effective action to depend upon the gauge on-shell which conflicts with the statements of the general theorems on gauge dependence [21,22]. There have been papers either maintaining the result [23] and giving reasons for possible gauge dependence in arbitrary non-renormalizable gauge theories [24] or expressing a doubt [25] about the applicability of the general statements [21,22], as formal ones, to specific theories (Einstein gravity, in particular). The study of Ref.…”

Section: Introductionmentioning

confidence: 99%