Perfect fluid coupled to a solenoidal field which enjoys the \(\ell\)-conformal Galilei symmetry. (English) Zbl 07846325
Summary: A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter \(\kappa\) and in the particular case of \(\kappa = 1\) it describes a perfect fluid coupled to a magnetic field. For a special value of \(\kappa\), the theory admits the Schrödinger symmetry group which is consistent with the magnetic case in two spatial dimensions only. Generalization to the case of the \(\ell\)-conformal Galilei group for an arbitrary half-integer parameter \(\ell\) is constructed.
References:
| [1] | Rangamani, M., Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quantum Gravity, 26, Article 224003 pp., 2009 · Zbl 1181.83005 |
| [2] | Son, D. T., Toward an AdS/cold atoms correspondence: a geometric realization of the Schrodinger symmetry, Phys. Rev. D, 78, Article 046003 pp., 2008 |
| [3] | Balasubramanian, K.; McGreevy, J., Gravity duals for non-relativistic CFTs, Phys. Rev. Lett., 101, Article 061601 pp., 2008 · Zbl 1228.81247 |
| [4] | Nishida, Y.; Son, D. T., Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories, Lect. Notes Phys., 836, 233, 2012 |
| [5] | Henkel, M., Local scale invariance and strongly anisotropic equilibrium critical systems, Phys. Rev. Lett., 78, 1940, 1997 |
| [6] | Negro, J.; del Olmo, M. A.; Rodriguez-Marco, A., Nonrelativistic conformal groups, J. Math. Phys., 38, 3786, 1997 · Zbl 0903.70012 |
| [7] | Niederer, U., The maximal kinematical invariance group of the free Schrödinger equation, Helv. Phys. Acta, 45, 802-810, 1972 |
| [8] | Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J., Exotic Galilean conformal symmetry and its dynamical realisations, Phys. Lett. A, 357, 1, 2006 · Zbl 1236.81129 |
| [9] | Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J., Acceleration-extended Galilean symmetries with central charges and their dynamical realizations, Phys. Lett. B, 650, 203, 2007 · Zbl 1248.81069 |
| [10] | Duval, C.; Horvathy, P., Non-relativistic conformal symmetries and Newton-Cartan structures, J. Phys. A, 42, Article 465206 pp., 2009 · Zbl 1180.37078 |
| [11] | Fedoruk, S.; Ivanov, E.; Lukierski, J., Galilean conformal mechanics from nonlinear realizations, Phys. Rev. D, 83, Article 085013 pp., 2011 |
| [12] | Duval, C.; Horvathy, P., Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes, J. Phys. A, 44, Article 335203 pp., 2011 · Zbl 1223.70060 |
| [13] | Gomis, J.; Kamimura, K., Schrodinger equations for higher order non-relativistic particles and N-Galilean conformal symmetry, Phys. Rev. D, 85, Article 045023 pp., 2012 |
| [14] | Galajinsky, A.; Masterov, I., Dynamical realization of ℓ-conformal Galilei algebra and oscillators, Nucl. Phys. B, 866, 212, 2013 · Zbl 1262.37024 |
| [15] | Andrzejewski, K.; Gonera, J.; Kosinski, P.; Maslanka, P., On dynamical realizations of ℓ-conformal Galilei groups, Nucl. Phys. B, 876, 309, 2013 · Zbl 1284.37045 |
| [16] | Chernyavsky, D.; Galajinsky, A., Ricci-flat spacetimes with ℓ-conformal Galilei symmetry, Phys. Lett. B, 754, 249, 2016 · Zbl 1367.53065 |
| [17] | O’Raifeartaigh, L.; Sreedhar, V. V., The maximal kinematical invariance group of fluid dynamics and explosion-implosion duality, Ann. Phys., 293, 215, 2001 · Zbl 1071.76556 |
| [18] | Jackiw, R.; Nair, V. P.; Pi, S. Y.; Polychronakos, A. P., Perfect fluid theory and its extensions, J. Phys. A, 37, R327, 2004 · Zbl 1072.76004 |
| [19] | Horvathy, P. A.; Zhang, P.-M., Non-relativistic conformal symmetries in fluid mechanics, Eur. Phys. J. C, 65, 607, 2010 |
| [20] | Galajinsky, A., Equations of fluid dynamics with the ℓ-conformal Galilei symmetry, Nucl. Phys. B, 984, Article 115965 pp., 2022 · Zbl 1514.81223 |
| [21] | Galajinsky, A., The group-theoretic approach to perfect fluid equations with conformal symmetry, Phys. Rev. D, 107, 2, Article 026008 pp., 2023 |
| [22] | Snegirev, T., Hamiltonian formulation for perfect fluid equations with the ℓ-conformal Galilei symmetry, J. Geom. Phys., 192, Article 104930 pp., 2023 · Zbl 1541.70031 |
| [23] | Landau, L. D.; Lifshitz, E. M., Electrodynamics of Continuous Media, 1960, Pergamon Press · Zbl 0122.45002 |
| [24] | Morrison, P. J.; Greene, J. M., Noncanonical Hamiltonian density formulation of hydrodynamics and ideal magnetohydrodynamics, Phys. Rev. Lett., 45, 790, 1980 |
| [25] | Galajinsky, A.; Masterov, I., Remarks on l-conformal extension of the Newton-Hooke algebra, Phys. Lett. B, 702, 265-267, 2011 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
