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. 
@article{TRSPY_1999_226_a15,
     author = {R. Jackiw and A. P. Polychronakos},
     title = {Dynamical {Poincar\'e} {Symmetry} {Realized} by {Field-Dependent} {Diffeomorphisms}},
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     publisher = {mathdoc},
     volume = {226},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_1999_226_a15/}
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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/