A new formulation of non-relativistic diffeomorphism invariance

Banerjee, Rabin; Mitra, Arpita; Mukherjee, Prerana

doi:10.1016/j.physletb.2014.09.004

Cited by 65 publications

(152 citation statements)

References 20 publications

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“…We now develop a formalism in which the diffeomorphism invariance is explicit at each stage of the calculation. That formalism is a version of Newton-Cartan geometry, which has been previously applied to the quantum Hall problem was developed first in the context of nonrelativistic gravity by Cartan [25,26] and may be viewed as the natural structure preserved by a gauging of Galilean symmetry [27,28].…”

Section: Newton-cartan Geometry With Torsionmentioning

confidence: 99%

Spacetime symmetries of the quantum Hall effect

et al. 2015

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We study the symmetries of nonrelativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the nonrelativistic diffeomorphism invariance studied in previous work is enhanced to a full spacetime symmetry, allowing us to derive a number of Ward identities. These symmetries are smooth in the massless limit of the lowest Landau level. We develop a formalism for Newton-Cartan geometry with torsion to write these Ward identities in a covariant form. Previous results on the connection between Hall viscosity and Hall conductivity are reproduced.

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Section: Newton-cartan Geometry With Torsionmentioning

confidence: 99%

Spacetime symmetries of the quantum Hall effect

et al. 2015

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“…(1) was assumed. The powerful apparatus of localizing the symmetry, introduced for Poincaré symmetry by Utiyama [32][33][34][35][36][37] and recently generalized to different contexts [38][39][40][41][42][43], was then applied in [31] to couple the Galileon model with gravity in curved spacetime which retains both the properties, namely, invariance under covariant Galileon symmetry and absence of Ostrogradsky ghosts. The covariant Galileon model thus constructed involves auxiliary fields corresponding to the localization of Poincaré (spacetime) and Galileon (internal) symmetries.…”

Section: Introductionmentioning

confidence: 99%

Cosmological implications of a shift symmetric Galileon field

et al. 2017

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A ghost-free metric formulation of the recently proposed covariant Galileon model [31] which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileon Lagrangian, allows us to include an appropriate potential term which can explain late time acceleration, in accordance with recent findings in the literature.

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“…In deriving the above we have made use of (23).We find (29) is exactly what GGT predicts [29]. The above action represents the coupling of nonrelativistic matter with NC background metric.…”

Section: Galilean Gauge Theory and Newton Cartan Spacetimementioning

confidence: 56%

Torsional Newton–Cartan geometry from Galilean gauge theory

Banerjee

Mukherjee²

2016

Class. Quantum Grav.

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Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton Cartan geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphisn [16,32] is focussed from a new angle. The expression of the torsionful connection is worked out which is in complete parallel with the relativistic theory. Also smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the Newton Cartan spacetime is provided where the first order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression.

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A new formulation of non-relativistic diffeomorphism invariance

Cited by 65 publications

References 20 publications

Spacetime symmetries of the quantum Hall effect

Spacetime symmetries of the quantum Hall effect

Cosmological implications of a shift symmetric Galileon field

Torsional Newton–Cartan geometry from Galilean gauge theory

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