Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Papageorgiou, Georgios K.; Schroers, Bernd J.

doi:10.1007/jhep11(2010)020

Cited by 46 publications

(96 citation statements)

References 42 publications

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“…It is worth stressing that the connection between the Poisson-Lie group approach presented here and the role that classical -matrices and Drinfel' d-doubles play in the context of 2 + 1 quantum gravity [76][77][78][79][80][81][82][83][84] has been studied in detail in the works [85][86][87][88][89]. Also, the deformed Casimir operators (57) (or (64)) can be used to provide modified dispersion relations, which should be related to those appearing in several phenomenological approaches to quantum gravity (see [90][91][92][93]).…”

Section: Discussionmentioning

confidence: 92%

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

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The -deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel' d-double and the Poisson-Lie structure underlying the -deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson-Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the -Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of "duality" between the cosmological constant and the Planck scale is also envisaged.

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Section: Discussionmentioning

confidence: 92%

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Ballesteros

Bruno

Herranz

2017

Advances in High Energy Physics

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“…Following Fock-Rosly construction [77,78], in such framework we describe gravitational degrees of freedom as parameterizing the Poisson-Lie group manifold. If we search for quantum deformations of Fock-Rosly construction, it appears that only classical r-matrices obtained from Drinfeld double (DD) structures [10,11] are allowed [79][80][81]. The DD structures and corresponding classical r-matrices for o(3, 1) and o(2, 2) algebras were recently constructed and classified [74][75][76].…”

Section: Jhep11(2017)187mentioning

confidence: 99%

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Borowiec¹,

Lukierski²,

Tolstoy³

2017

J. High Energ. Phys.

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We construct firstly the complete list of five quantum deformations of D = 4 complex homogeneous orthogonal Lie algebra o(4; C) ∼ = o(3; C) ⊕ o(3; C), describing quantum rotational symmetries of four-dimensional complex space-time, in particular we provide the corresponding universal quantum R-matrices. Further applying four possible reality conditions we obtain all sixteen Hopf-algebraic quantum deformations for the real forms of o(4; C): Euclidean o(4), Lorentz o(3, 1), Kleinian o(2, 2) and quaternionic o ⋆ (4). For o(3, 1) we only recall well-known results obtained previously by the authors, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) as well as for the complex Lie algebra o(4; C) we present new results.

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“…The NR theories have received a renewed interest since they play an important role to approach condensed matter systems [8][9][10][11][12][13][14][15] and NR effective field theories [16][17][18][19]. It seems then natural to extend NR gravity theories [20][21][22][23][24][25][26][27][28][29][30][31][32][33] to the presence of supersymmetry. In particular, NR supergravity models can be seen as a starting point to approach supersymmetric field theories on curved backgrounds by means of localization [34,35].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

Concha

Ravera

Rodríguez

2020

J. High Energ. Phys.

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We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the nonrelativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

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Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Cited by 46 publications

References 42 publications

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Three-dimensional Maxwellian extended Bargmann supergravity

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