Not so non-renormalizable gravity

Kreimer, Dirk

doi:10.1090/conm/539/10637

Cited by 5 publications

(7 citation statements)

References 23 publications

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“…While, at the other end of the scale, exceptionally good infrared behaviour could mimic both "dark matter" and "dark energy" behaviour. • In relation with the discussion at the end of subsection 3.6, support for the idea that UV divergences in gravity are not so intractable has come recently from work by Kreimer [54].…”

Section: Other Waysmentioning

confidence: 86%

Notes on “Quantum Gravity” and Noncommutative Geometry

Gracia‐Bondía

2010

Lecture Notes in Physics

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I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Section 3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 4 briefly deals with the unimodular variants. Section 5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing; which justifies the place granted to the reconstruction theorem. Together with Section 3, this part constitutes the main body of the notes. Only very summarily at the end of this section we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

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Section: Other Waysmentioning

confidence: 86%

Notes on “Quantum Gravity” and Noncommutative Geometry

Gracia‐Bondía

2010

Lecture Notes in Physics

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“…All local QFTs of physical interest are one-loop divergent, in particular all QFTs from the Standard Model (as they are renormalizable) and Quantum General Relativity, viewed as an effective QFT, (a simple combinatorial argument shows, that the superficial degree of divergence of a Feynman graph is independent of its residue and depends only on its loop number, and is in particular already divergent for one-loop Feynman graphs, c.f. [28,29]). In the case of local QFTs which are not one-loop divergent Equations ( 75) and (77) need to be corrected to (for simplicity, we assume that G r ∈ H Q is a sum of products of Feynman graphs with residue r ∈ R Q -otherwise the correcting sums depend also on the different residues and also products between them need to be considered)…”

Section: A Superficial Argumentmentioning

confidence: 99%

“…Theorem 5.4 describes the most general situation. Slightly less general results in this direction can be found in [7,8,9,10,11,28,29,31], some of them using the language of Hochschild cohomology.…”

Section: Quantum Gauge Symmetries and Subdivergencesmentioning

confidence: 99%

Gauge Symmetries and Renormalization

Prinz¹

2020

Preprint

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The preservation of gauge symmetries to the quantum level induces symmetries between renormalized Green's functions. These symmetries are known by the names of Ward-Takahashi and Slavnov-Taylor identities. On a perturbative level, these symmetries can be implemented as Hopf ideals in the Connes-Kreimer renormalization Hopf algebra. In this article, we generalize the existing literature to the most general case by first motivating these symmetries on a generic level and then proving that they indeed generate Hopf ideals, where we also include the more involved cases of super-and non-renormalizable local QFTs. Finally, we provide a criterion for their validity on the level of renormalized Feynman rules.

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“…Loop Quantum Gravity, String Theory or Supergravity. In this article we continue the work on perturbative QGR as started by D. Kreimer in the 2000s [11,12]. D. Kreimer used the modern techniques of Hopf algebraic renormalization developed by A. Connes and himself in the 1990s and 2000s [13,14,15].…”

Section: Introductionmentioning

confidence: 96%

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Prinz

2021

Annals of Physics

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This article is an extension of the authors second master thesis [1]. It aims to introduce the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry's Theorem. Next, the restricted combinatorial Green's functions for all two-loop propagator and all one-loop divergent subgraphs thereof are presented. Finally, relations between these oneloop restricted combinatorial Green's functions necessary for multiplicative renormalization are discussed. One of those relations suggests that it is unphysical to consider the coupling to Spinor Electrodynamics alone and instead consider the coupling to the whole Electroweak Sector.

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Not so non-renormalizable gravity

Abstract: Abstract. We review recent progress with the understanding of quantum fields, including ideas [1] how gravity might turn out to be a renormalizable theory after all.

Cited by 5 publications

References 23 publications

Notes on “Quantum Gravity” and Noncommutative Geometry

Notes on “Quantum Gravity” and Noncommutative Geometry

Gauge Symmetries and Renormalization

Algebraic Structures in the Coupling of Gravity to Gauge Theories

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