Geodesic
Dynamical Poincar\'e Symmetry Realized by Field-Dependent Diffeomorphisms
Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 193-211.

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We present several Galileo invariant Lagrangians, which are invariant against Poincaré transformations defined in one higher (spatial) dimension. Thus these models, which arise in a variety of physical situations, provide a representation for a dynamical (hidden) Poincaré symmetry. The action of this symmetry transformation on the dynamical variables is nonlinear, and in one case involves a peculiar field-dependent diffeomorphism. Some of our models are completely integrable, and we exhibit explicit solutions. 
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R. Jackiw; A. P. Polychronakos. Dynamical Poincar\'e Symmetry Realized by Field-Dependent Diffeomorphisms. Informatics and Automation, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 193-211. http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a15/

[1] Faddeev L., Jackiw R., “Hamiltonian reduction of unconstrained and constrained systems”, Phys. Rev. Lett., 60 (1988), 1692–1694 | DOI | MR | Zbl

[2] Eckart C., “The electrodynamics of material media”, Phys. Rev., 54 (1938), 920–923 | DOI

[3] Schakel A., Effective field theory of ideal-fluid hydrodynamics, Preprint, 1996; arXiv: cond-mat/9607164

[4] Ogawa N., A note of gauge principle and spontaneous symmetry breaking in classical particle mechanics, Preprint, 1998; arXiv: 9801115

[5] Landau L., Lifschitz E., Fluid mechanics, 2-nd ed., Pergamon Press, Oxford (UK), 1987 | MR | Zbl

[6] Madelung E., “Quantentheorie in hydrodynamischer Form”, Ztschr. Phys., 40 (1926), 322–326 | DOI | Zbl

[7] Merzbacher E., Quantum mechanics, 3-rd ed., Wiley, N. Y., 1998 | MR

[8] Jevicki A., Phys. Rev. D, 57 (1998), 5955 | DOI

[9] Hoppe J., Quantum theory of a massless relativistic surface and ... , MIT PhD. Thes., 1982

[10] Bordemann M., Hoppe J., “The dynamics of relativistic membranes. Reduction to 2-dimensional fluid dynamics”, Phys. Lett. B, 317 (1993), 315–320 | DOI | MR

[11] Jackiw R., “Introducing scale symmetry”, Phys. Today, 25:1 (1972), 23–27 | DOI

[12] Hagen C., “Scale and conformal transformations in Galilean-covariant field theory”, Phys. Rev. D, 5 (1972), 377–388 | DOI

[13] Niederer U., “The maximal kinematical invariance group of the free Schrödinger equation”, Helv. phys. acta, 45 (1972), 802–810 | MR

[14] Niederer U., “The maximal kinematical invariance group of the harmonic oscillator”, Helv. phys. acta, 46 (1973), 191–200

[15] Niederer U., “The maximal kinematical invariance group of Schrödinger equations with arbitrary potentials”, Helv. phys. acta, 47 (1974), 167–172 | MR

[16] Niederer U., “Schrödinger invariant generalized heat equations”, Helv. phys. acta, 51 (1978), 220–239 | MR

[17] Susskind L., “Model of self-induced strong interactions”, Phys. Rev., 165 (1968), 1535–1554 | DOI

[18] Bazeia D., Jackiw R., “Nonlinear realization of a dynamical Poincaré symmetry by a field-dependent diffeomorphism”, Ann. Phys., 270:1 (1998), 246–259 ; arXiv: hep-th/9803165 | DOI | MR | Zbl