*‐Lie derivative, *‐covariant derivative and *‐gravity

Aschieri, Paolo

doi:10.1002/prop.200610389

Cited by 9 publications

(4 citation statements)

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“…Twisted deformations in this broader context are a step forward in the geometrization of the traditional Drinfeld scheme [35]. It has been argued in a seminal paper [18] (see also [13,39,54]) that such a framework is very useful in noncommutative geometry and deformed field theories and gives a hope to describe gravity at the Planck scale 1 .…”

Section: Preliminaries and Notationmentioning

confidence: 99%

κ-Minkowski spacetime as the result of Jordanian twist deformation

2009

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Two one-parameter families of twists providing κ−Minkowski * -product deformed spacetime are considered:Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of "deformed realizations" of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers κ−Poincaré dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincaré algebra) takes an energy-dependent linear mass deformation form.

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Section: Preliminaries and Notationmentioning

confidence: 99%

κ-Minkowski spacetime as the result of Jordanian twist deformation

2009

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“…Moreover, the theory is also invariant under the action of deformed diffeomorphisms. These are -deformations of infinitesimal diffeomorphisms, obtained by composing the Lie derivative with the twist [17,25]. The proof of the invariance of the action (2.74) under infinitesimal -diffeomorphisms is a straightforward generalization of the one given in [11,32] for the noncommutative Palatini action.…”

Section: Symmetries: Deformed Gauge Invariance and Dualitymentioning

confidence: 96%

“…In the following, we consider the full Palatini-Holst action, within the same geometric framework. The noncommutative structure is obtained via a twist-deformation of the differential geometry [17,25,26], which allows to build from first principles a modified theory of gravity having Planck scale modifications naturally built-in. There are two independent sources of new physical effects that may arise in such theories.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative gravity with self-dual variables

Cesare

Sakellariadou

Vitale³

2018

Class. Quantum Grav.

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We build a noncommutative extension of Palatini-Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani.The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. The model is shown to exhibit new duality symmetries. The introduction of the Holst term leads to a dramatic simplification of the dynamics, which is achieved when the Barbero-Immirzi parameter takes the value β = −i, corresponding to a self-dual action. We study in detail the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. The effects of spacetime noncommutativity are taken into account perturbatively, and are computed explicitly in a simple example. Connections with bimetric theories and the role of local conformal invariance in the commutative limit are also explored.

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“…Namely, noncommutativity also affects the geometric or "pure" gravity side of the Einstein's equation. In numerous approaches [56][57][58][59][60][61][62][63] we have witnessed the NC corrections to Einstein's equation. Moreover, in [64][65][66] it has been indicated that the nature of the cosmological constant could be entirely noncommutative.…”

Section: Final Remarksmentioning

confidence: 99%