Dynamical Poincare Symmetry Realized by Field-dependent Diffeomorphisms

Abstract

We present several Galileo invariant Lagrangians, which are invariant against Poincare 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) Poincare 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.

Contribution to Faddeev Festschrift, Steklov Mathematical Institute Proceedings; REVTeX, BoxedEPS.tex, 5 figures, 21 pages; email to jackiw@mitlns.mit.edu