Nonlinear realization of a dynamical poincare symmetry by a field-dependent diffeomorphism

We consider a description of membranes by (2, 1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant syste ms, as well as others related to them, admit a peculiar diffeomorphism symm etry, where the transformation rule for coordinates involves the fields. Th e symmetry algebra coincides with that of the Poincare group in one higher dimension. Therefore, these models provide a nonlinear representation for a dynamical Poincare group. (C) 1998 Academic Press.