Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

By C. Duval, G. W. Gibbons, P. Horváthy, Pengming Zhang. 2014

371 citations recorded by the source corpus.

The Carroll group was originally introduced by Lévy-Leblond (1965 Ann. Inst. Henri Poincaré 3 1) by considering the contraction of the Poincaré group as c → 0. In this paper an alternative definition, based on the geometric properties of a non-Minkowskian, non-Galilean but nevertheless boost-invariant, spacetime structure is proposed. A ‘duality’ with the Galilean limit c → ∞ is established. Our theory is illustrated by Carrollian electromagnetism.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/08161013f327b83bcc391247759d5061d8e4e89d

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Citations in the corpus

Flat holography and Carrollian fluids (2018, background): “ic. From a representative of this class, we must be able to explore others by Weyl transformations, and this amounts to study conformal Carrollian geometry as opposed to plain Carrollian geometry(see [48]). The action of Weyl transformations on the elements of the Carrollian geometry on a surface Si”
Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids (2018, background): “Carrollian physics has attracted some attention over the recent years [12, 13].”
Flat holography: aspects of the dual field theory (2016, background): “[61] to revisit our present analysis in order to present a more geometric picture of the theories we have discussed.”
Conformal Carroll groups (2014, methodology): “In our previous paper [8] we constructed massive particle models with Carroll symmetry using Souriauʼs method [18].”
Carrollian physics at the black hole horizon (2019, background): “Actually, it is now understood that any null hypersurface is endowed with a Carrollian geometry1 [10,12–16] and that the associated constraint equations are ultra-relativistic conservation laws [17].”
Conformal Carroll groups and BMS symmetry (2014, methodology): “, the flat Carroll structure (i) we get the usual Carroll group [5], denoted by Carr(d + 1) in [7].”
Bridging Carrollian and celestial holography (2022, background): “In particular, this tells us that the propagator of source operators is u-dependent, which suggests that the source sector of the Carrollian CFT is a timelike electric-type of Carrollian theory [42,47,190,228,229].”
Gauging the Carroll algebra and ultra-relativistic gravity (2015, methodology): “The TNC metric-like objects are given by τμ and hμν whereas the Carrollian metric-like objects are given by v μ and hμν suggesting the duality [26]”
Carroll structures, null geometry, and conformal isometries (2019, background): “At this point of the presentation, it is worth mentioning that the triple (C, V, g) corresponds to the definition of a weak Carrollian structure given in [2].”
Carroll versus Galilei gravity (2017, background): “In [29], ‘Carrollian electromagnetism of the magnetic type’ is also considered, whose Lagrangian is given by ~ B · ~ B.”
Tensionless strings from worldsheet symmetries (2015, background): “The tensionless worldsheet, which is what the worldsheet becomes near the Hagedorn temperature, is now replaced by a Carrollian manifold [47, 48].”
Carroll contractions of Lorentz-invariant theories (2021, methodology): “The same difference in transformation rules was observed and analyzed in the case of electromagnetism, where again, the electric theory was naturally found to correspond to a formulation involving fields transforming in covariant representations, while the magnetic theory was found to correspond to ”
Dynamics of Carroll particles (2014, methodology): “25) τ = ξ μ  If curvature is turned on by hand this condition should be supplemented with the requirement that g 0 ij = ξ  , where gij is the (non-flat) metric of the transverse space [12].”