A free Lie algebra approach to curvature corrections to flat space-time

Gomis, Joaquim; Kleinschmidt, Axel; Roest, Diederik; Salgado-Rebolledo, Patricio

doi:10.1007/jhep09(2020)068

Cited by 5 publications

(11 citation statements)

References 36 publications

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“…This property makes it different from a phenomenological algebra introduced recently in[43] for the description of curvature corrections to the isometry algebra of flat space-time. Another difference is that in our case all embeddings have two common elements l0 and T0.…”

mentioning

confidence: 81%

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Borowiec

Brocki

Kowalski-Glikman

et al. 2021

J. High Energ. Phys.

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BMS symmetry is a symmetry of asymptotically flat spacetimes in vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been noted in the 3 dimensional case only. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.

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mentioning

confidence: 81%

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Borowiec

Brocki

Kowalski-Glikman

et al. 2021

J. High Energ. Phys.

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“…A similar construction can be found e.g. in[60] where curvature corrections to flat space-time were studied.…”

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confidence: 83%

Colourful Poincaré symmetry, gravity and particle actions

Gomis

Joung

Kleinschmidt

et al. 2021

J. High Energ. Phys.

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We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

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“…The small parameter can also be taken to be the curvature of space-time in appropriate dimensions. This was considered in [68] and leads to corrections to Minkowski space-time towards (Anti-)de Sitter space when the starting point is the (A)dS algebra that differs from the Poincaré algebra (2.1) by the non-trivial commutator…”

Section: Post-minkowski Space-timementioning

confidence: 99%

“…The transformations formula for these coordinates is now more complicated since the underlying translations no longer commute due to (3.33). Since we do not rely on them in the following, we refer the reader to [68]. In section 4.5 we shall study a particle model based on this generalised space-time.…”

Section: Post-minkowski Space-timementioning

confidence: 99%

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Infinite-dimensional algebras as extensions of kinematic algebras

Gomis¹,

Kleinschmidt²

2022

Preprint

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Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits of a relativistic system, including both the Galilei and the Carroll limit. We develop a framework that captures systematically the corrections to the strict non-relativistic limit by introducing new infinite-dimensional algebras, with emphasis on the Carroll case. One of our results is to highlight a new type of duality between Galilei and Carroll limits that extends to corrections as well. We realise these algebras in terms of particle models. Other applications include curvature corrections and particles in a background electro-magnetic field.

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A free Lie algebra approach to curvature corrections to flat space-time

Cited by 5 publications

References 36 publications

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

Colourful Poincaré symmetry, gravity and particle actions

Infinite-dimensional algebras as extensions of kinematic algebras

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