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Conformal Anisotropic Mechanics · Around

2009

Conformal Anisotropic Mechanics

Romero, Juan M., Cuesta, Vladimir, Garcia, J. Antonio et al.

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In this paper we implement scale anisotropic transformations in the space-time in classical mechanics.

The resulting system is consistent with the dispersion relation of gravity at a Lifshitz point recently considered in arXiv:0901.3775.
Also, we show that our model is a generalization of the conformal mechanics of Alfaro, Fubini and Furlan.
For arbitrary $z$ we construct the dynamical symmetries that correspond to the Schroedinger algebra.

Built on

C. R. Hagen, “Scale and conformal transformations in galilean-covariant field theory,” Phys. Rev. D 5
1972
Earlier work this paper cites.
V. Alfaro, S. Fubini, G. Furlan, Conformal Invariance in Quantum Mechanics,
1976
Earlier work this paper cites.
P.C. Hohenberg, B.I. Halperin, Theory of Dynamic Critical Phenomena,
1977
Earlier work this paper cites.
C. Teitelboim, Quantum Mechanics of the Gravitational Field,
1982
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M. Henneaux and C. Teitelboim, Quantization of Gauge System,
1992
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J. L. Cardy, Scaling And Renormalization In Statistical Physics,
1996
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Then

J.L.F. Barbon, C.A. Fuertes On the spectrum of nonrelativistic AdS/CFT,
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D. T. Son, “Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry,” Phys. Rev. D 78
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K. Balasubramanian and J. McGreevy, “Gravity duals for non-relativistic CFTs,” Phys. Rev. Lett. 101
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P. Horava, Quantum Gravity at a Lifshitz Point,
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A. Bagchi and R. Gopakumar, “Galilean Conformal Algebras and AdS/CFT,” JHEP 0907
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