Classical and quantum gravity with fractional operators

Calcagni, Gianluca

doi:10.48550/arxiv.2106.15430

Cited by 4 publications

(11 citation statements)

References 74 publications

(129 reference statements)

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“…In [39], we compare this and the other types of dimensional flow discussed in sections 3.3.3 and 3.4.3 with the dimensional flow found in quantum gravity.…”

Section: Dimensional Flowmentioning

confidence: 85%

“…For this theory, the quantum properties in the UV are the same as an ordinary QFT, so that there is no chance that renormalizability is improved. However, if * is large enough the theory can work as a model with IR modifications which, in the case of gravity, can have interesting consequences at the cosmological level [39]. • A third possibility is to extend the multi-fractional kinetic operator (48) to three operators with three different exponents and two scales 1 < 2 :…”

Section: Dimensional Flowmentioning

confidence: 99%

“…While T[∂ γ ] and T[ γ ] have constant Hausdorff and spectral dimension, the dimensional flow of all the other theories is the same, with a constant Hausdorff dimension and a varying spectral dimension. We will carry out a systematic study in the case of a real scalar field theory, which is a good training ground in preparation for gravity, which is touched upon in a companion paper [39].…”

Section: Introductionmentioning

confidence: 99%

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Quantum scalar field theories with fractional operators

Calcagni

2021

Class. Quantum Grav.

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We explore quantum field theories with fractional d'Alembertian γ . Both a scalar field theory with a derivative-dependent potential and gauge theory are strictly renormalizable for a fractional power 1 < γ 2, super-renormalizable for γ > 2 and finite if one introduces killer operators. Unitarity is achieved by splitting the kinetic term into the product of massive fractional operators, eventually sending the masses to zero if so desired. Fractional quantum gravity is also discussed and found to be strictly renormalizable for 2 γ 4 and super-renormalizable for γ > 4. To make it unitary, we combine the splitting procedure with a fractional generalization of the Anselmi-Piva prescription for fakeons. Among new technical results with wider applications, we highlight the Leibniz rule for arbitrary powers of the d'Alembertian and the Källén-Lehmann representation for a propagator with an arbitrary number of branch cuts. 6.2.4 N 4 cuts 45 7 Fractional gravity 47 7.1 Graviton action 47 7.2 Generalized power counting 48 7.3 Finiteness 50 7.4 Double splitting and unitarity 51 8 Discussion 53 A Leibniz rule for powers of the d'Alembertian 55 A.1 Leibniz rule for integer powers n 56 A.2 Leibniz rule for arbitrary powers γ 57 B Useful results in BV formalism 59 B.1 Traces of fractional operators: first term in eq. (3.23) 59 B.2 Traces of fractional operators: second term in eq. (3.23) 60 B.3 Discontinuity at γ = 1 60 C Calculation of ρ i 62 D No-go theorem on the Källén-Lehmann representation 63

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“…In [39], we compare this and the other types of dimensional flow discussed in sections 3.3.3 and 3.4.3 with the dimensional flow found in quantum gravity.…”

Section: Dimensional Flowmentioning

confidence: 85%

Section: Dimensional Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum scalar field theories with fractional operators

Calcagni

2021

Class. Quantum Grav.

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“…Other avenues to explore in the future may come across other multi-fractional theories, those with fractional operators [13,41]. A phenomenological Newtonian model with fractional Laplacian seems able to fit galaxy rotation curves [21,22] but it has not been embedded in a covariant theory.…”

Section: Discussionmentioning

confidence: 99%

Gravitational potential and galaxy rotation curves in multi-fractional spacetimes

Calcagni

Varieschi

2022

J. High Energ. Phys.

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Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes with variable Hausdorff and spectral dimension, originally proposed as descriptions of geometries arising in quantum gravity. We derive the Poisson equation and the Newtonian potential of these theories starting from their covariant modified Einstein’s equations. In particular, in the case of the theory Tv with weighted derivatives with small fractional corrections, we find a gravitational potential that grows logarithmically at large radii when the fractional exponent takes the special value α = 4/3. This behaviour is associated with a restoration law for the Hausdorff dimension of spacetime independently found in the dark-energy sector of the same theory. As an application, we check whether this potential can serve as an alternative to dark matter for the galaxies NGC7814, NGC6503 and NGC3741 in the SPARC catalogue. We show that their rotation curves at medium-to-large radii can indeed be explained by purely geometric effects, although the Tully-Fisher relation is not reproduced well. We discuss how to fix the small-radius behaviour by lifting some approximations and how to test the model with other observables and an enlarged galaxy sample.

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“…Apart from the simplicial methods described in §4.2 and a few proposals for small generalizations of manifold structure [21][22][23], there has been fairly little work on this prospect within conventional quantum gravity. There has, however, been a research program aimed at understanding properties of field theories in spaces with fractal dimensions [184][185][186][187], and perhaps their implications for quantum gravity [188].…”

Section: • Fractal Spacetimesmentioning

confidence: 99%